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1.
TranslationInvariance of TwoDimensional Gibbsian Systems of Particles with Internal Degrees of Freedom, preprint, 2006. Available online from http://www....
Open Access
Title:
TranslationInvariance of TwoDimensional Gibbsian Systems of Particles with Internal Degrees of Freedom, preprint, 2006. Available online from http://www. arxiv.org/abs/math.PR/0603140
Author:
Thomas Richthammer
Thomas Richthammer
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Description:
The conservation of translation as a symmetry in twodimensional systems with interaction is a classical subject of statistical mechanics. Here we establish such a result for Gibbsian systems of marked particles with twobody interaction, where the interesting cases of singular, hardcore and discontinuous interaction are included. We start with...
The conservation of translation as a symmetry in twodimensional systems with interaction is a classical subject of statistical mechanics. Here we establish such a result for Gibbsian systems of marked particles with twobody interaction, where the interesting cases of singular, hardcore and discontinuous interaction are included. We start with the special case of a finite state Widom Rowlinson potential in order to show how to treat hard cores in general. Key words: Gibbsian point processes, MerminWagner theorem, translation, hardcore potential, singular potential, Widom Rowlinson potential
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The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20121106
Source:
http://arxiv.org/pdf/math/0603140v2.pdf
http://arxiv.org/pdf/math/0603140v2.pdf
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Document Type:
text
Language:
en
Subjects:
percolation
percolation
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.236.4339
http://arxiv.org/pdf/math/0603140v2.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.236.4339
http://arxiv.org/pdf/math/0603140v2.pdf
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2.
degrees of freedom
Open Access
Title:
degrees of freedom
Author:
Thomas Richthammer
Thomas Richthammer
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Description:
Gibbsian systems of particles with internal
Gibbsian systems of particles with internal
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The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20121106
Source:
http://arxiv.org/pdf/math/0603140v3.pdf
http://arxiv.org/pdf/math/0603140v3.pdf
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Document Type:
text
Language:
en
Subjects:
Key words ; Gibbsian point processes ; MerminWagner theorem ; translation ; hard core ; singularity ; Widom Rowlinson potential ; Potts model ; percolation
Key words ; Gibbsian point processes ; MerminWagner theorem ; translation ; hard core ; singularity ; Widom Rowlinson potential ; Potts model ; percolation
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.236.1605
http://arxiv.org/pdf/math/0603140v3.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.236.1605
http://arxiv.org/pdf/math/0603140v3.pdf
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3.
. Stochastic
Open Access
Title:
. Stochastic
Author:
Sebastian Carstens
;
Thomas Richthammer
Sebastian Carstens
;
Thomas Richthammer
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Description:
We consider the model of Deijfen et al. for the competing growth of two d infection types in, based on the Richardson model on�d
We consider the model of Deijfen et al. for the competing growth of two d infection types in, based on the Richardson model on�d
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The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20121127
Source:
http://arxiv.org/pdf/0908.1551v1.pdf
http://arxiv.org/pdf/0908.1551v1.pdf
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text
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en
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Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.249.5006
http://arxiv.org/pdf/0908.1551v1.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.249.5006
http://arxiv.org/pdf/0908.1551v1.pdf
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4.
Twodimensional Gibbsian point processes with continuous spinsymmetries
Open Access
Title:
Twodimensional Gibbsian point processes with continuous spinsymmetries
Author:
Thomas Richthammer
Thomas Richthammer
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Description:
We consider twodimensional marked point processes which are Gibbsian with a twobodypotential of the form U = JV + K, where J and K depend on the positions and V depends on the marks of the two particles considered. V is supposed to have a continuous symmetry. We will generalise the famous MerminWagnerDobrushinShlosman theorem to this setti...
We consider twodimensional marked point processes which are Gibbsian with a twobodypotential of the form U = JV + K, where J and K depend on the positions and V depends on the marks of the two particles considered. V is supposed to have a continuous symmetry. We will generalise the famous MerminWagnerDobrushinShlosman theorem to this setting in order to show that the Gibbsian process is invariant under the given symmetry, when instead of smoothness conditions only continuity conditions are assumed. We will achieve this by using Ruelle’s superstability estimates and percolation arguments. 1
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The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20121101
Source:
http://arxiv.org/pdf/math/0407216v1.pdf
http://arxiv.org/pdf/math/0407216v1.pdf
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text
Language:
en
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Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.235.1924
http://arxiv.org/pdf/math/0407216v1.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.235.1924
http://arxiv.org/pdf/math/0407216v1.pdf
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5.
TranslationInvariance of TwoDimensional Gibbsian Systems of Particles with Internal Degrees of Freedom, preprint, 2006. Available online from http://www....
Open Access
Title:
TranslationInvariance of TwoDimensional Gibbsian Systems of Particles with Internal Degrees of Freedom, preprint, 2006. Available online from http://www. arxiv.org/abs/math.PR/0603140
Author:
Thomas Richthammer
Thomas Richthammer
Minimize authors
Description:
The conservation of translation as a symmetry in twodimensional systems with interaction is a classical subject of statistical mechanics. Here we establish such a result for Gibbsian particle systems with twobody interaction, where the interesting cases of singular, hardcore and discontinuous interaction are included. We start with the specia...
The conservation of translation as a symmetry in twodimensional systems with interaction is a classical subject of statistical mechanics. Here we establish such a result for Gibbsian particle systems with twobody interaction, where the interesting cases of singular, hardcore and discontinuous interaction are included. We start with the special case of pure hard core repulsion in order to show how to treat hard cores in general. Key words: Gibbsian point processes, MerminWagner theorem, translation, hardcore potential, singular potential, pure hard core repulsion
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The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20121204
Source:
http://arxiv.org/pdf/0706.3637v1.pdf
http://arxiv.org/pdf/0706.3637v1.pdf
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Document Type:
text
Language:
en
Subjects:
percolation
percolation
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Rights:
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.251.376
http://arxiv.org/pdf/0706.3637v1.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.251.376
http://arxiv.org/pdf/0706.3637v1.pdf
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6.
degrees of freedom
Open Access
Title:
degrees of freedom
Author:
Thomas Richthammer
Thomas Richthammer
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Description:
Gibbsian systems of particles with internal
Gibbsian systems of particles with internal
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20121105
Source:
http://arxiv.org/pdf/math/0603140v1.pdf
http://arxiv.org/pdf/math/0603140v1.pdf
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Document Type:
text
Language:
en
Rights:
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.235.7816
http://arxiv.org/pdf/math/0603140v1.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.235.7816
http://arxiv.org/pdf/math/0603140v1.pdf
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7.
TranslationInvariance of TwoDimensional Gibbsian Systems of Particles with Internal Degrees of Freedom, preprint, 2006. Available online from http://www....
Open Access
Title:
TranslationInvariance of TwoDimensional Gibbsian Systems of Particles with Internal Degrees of Freedom, preprint, 2006. Available online from http://www. arxiv.org/abs/math.PR/0603140
Author:
Thomas Richthammer
Thomas Richthammer
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Description:
One of the main objectives of equilibrium state statistical physics is to analyze which symmetries of an interacting particle system in equilibrium are broken or conserved. Here we present a general result on the conservation of translational symmetry for twodimensional Gibbsian particle systems. The result applies to particles with internal de...
One of the main objectives of equilibrium state statistical physics is to analyze which symmetries of an interacting particle system in equilibrium are broken or conserved. Here we present a general result on the conservation of translational symmetry for twodimensional Gibbsian particle systems. The result applies to particles with internal degrees of freedom and fairly arbitrary interaction, including the interesting cases of discontinuous, singular, and hard core interaction. In particular we thus show the conservation of translational symmetry for the continuum Widom Rowlinson model and a class of continuum Potts type models. Key words: Gibbs measures, MerminWagner theorem, translation, hard core, singularity, Widom Rowlinson model, Potts model, percolation.
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Year of Publication:
20121106
Source:
http://arxiv.org/pdf/math/0603140v4.pdf
http://arxiv.org/pdf/math/0603140v4.pdf
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Document Type:
text
Language:
en
Rights:
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.237.4136
http://arxiv.org/pdf/math/0603140v4.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.237.4136
http://arxiv.org/pdf/math/0603140v4.pdf
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8.
Proof of Aldous’ spectral gap conjecture
Open Access
Title:
Proof of Aldous’ spectral gap conjecture
Author:
Pietro Caputo
;
Thomas M. Liggett
;
Thomas Richthammer
Pietro Caputo
;
Thomas M. Liggett
;
Thomas Richthammer
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Description:
Abstract. Aldous ’ spectral gap conjecture asserts that on any graph the random walk process and the random transposition (or interchange) process have the same spectral gap. We prove the conjecture using a recursive strategy. The approach is a natural extension of the method already used to prove the validity of the conjecture on trees. The nov...
Abstract. Aldous ’ spectral gap conjecture asserts that on any graph the random walk process and the random transposition (or interchange) process have the same spectral gap. We prove the conjecture using a recursive strategy. The approach is a natural extension of the method already used to prove the validity of the conjecture on trees. The novelty is an idea based on electric network reduction, which reduces the problem to the proof of an explicit inequality for a random transposition operator involving both positive and negative rates. The proof of the latter inequality uses suitable coset decompositions of the associated matrices with rows and columns indexed by permutations. 1.
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Year of Publication:
20121127
Source:
http://arxiv.org/pdf/0906.1238v4.pdf
http://arxiv.org/pdf/0906.1238v4.pdf
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Document Type:
text
Language:
en
Rights:
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.249.7862
http://arxiv.org/pdf/0906.1238v4.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.249.7862
http://arxiv.org/pdf/0906.1238v4.pdf
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9.
Percolation of arbitrary words in one dimension
Open Access
Title:
Percolation of arbitrary words in one dimension
Author:
Geoffrey R. Grimmett
;
Thomas M. Liggett
;
Thomas Richthammer
Geoffrey R. Grimmett
;
Thomas M. Liggett
;
Thomas Richthammer
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Description:
We consider a type of longrange percolation problem on the positive integers, motivated by earlier work of others on the appearance of (in)finite words within a site percolation model. The main issue is whether a given infinite binary word appears within an iid Bernoulli sequence at locations that satisfy certain constraints. We settle the issu...
We consider a type of longrange percolation problem on the positive integers, motivated by earlier work of others on the appearance of (in)finite words within a site percolation model. The main issue is whether a given infinite binary word appears within an iid Bernoulli sequence at locations that satisfy certain constraints. We settle the issue in some cases, and provide partial results in others. 1
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Year of Publication:
20100117
Source:
http://www.statslab.cam.ac.uk/~grg/papers/grimmett6.pdf
http://www.statslab.cam.ac.uk/~grg/papers/grimmett6.pdf
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Document Type:
text
Language:
en
Rights:
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.151.7915
http://www.statslab.cam.ac.uk/~grg/papers/grimmett6.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.151.7915
http://www.statslab.cam.ac.uk/~grg/papers/grimmett6.pdf
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10.
Percolation of arbitrary words in one dimension
Open Access
Title:
Percolation of arbitrary words in one dimension
Author:
Geoffrey R. Grimmett
;
Thomas M. Liggett
;
Thomas Richthammer
Geoffrey R. Grimmett
;
Thomas M. Liggett
;
Thomas Richthammer
Minimize authors
Description:
We consider a type of longrange percolation problem on the positive integers, motivated by earlier work of others on the appearance of (in)finite words within a site percolation model. The main issue is whether a given infinite binary word appears within an iid Bernoulli sequence at locations that satisfy certain constraints. We settle the issu...
We consider a type of longrange percolation problem on the positive integers, motivated by earlier work of others on the appearance of (in)finite words within a site percolation model. The main issue is whether a given infinite binary word appears within an iid Bernoulli sequence at locations that satisfy certain constraints. We settle the issue in some cases, and provide partial results in others. 1
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Year of Publication:
20090916
Source:
http://www.statslab.cam.ac.uk/~grg/papers/finalglr.pdf
http://www.statslab.cam.ac.uk/~grg/papers/finalglr.pdf
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text
Language:
en
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Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.144.7638
http://www.statslab.cam.ac.uk/~grg/papers/finalglr.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.144.7638
http://www.statslab.cam.ac.uk/~grg/papers/finalglr.pdf
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(15) The Pennsylvania State University CiteSeerX...
(14) Thomas Richthammer
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(7) Thomas M. Liggett
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(7) mathematics probability
(6) 60k35
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(2) 60k35 secondary
(2) 82b21 primary
(2) 82b31
(2) 82b43
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(1) informatik und statistik
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(1) key words
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(1) mathematics combinatorics
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(1) new york
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(1) shape theorem
(1) singularity
(1) spectral gap
(1) translation
(1) weighted graph
(1) widom rowlinson potential
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(1) Physics [53*]
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