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Title:

Two-dimensional Gibbsian point processes with continuous spin-symmetries

Description:

We consider two-dimensional marked point processes which are Gibbsian with a two-body-potential 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 Mermin-Wagner-Dobrushin-Shlosman theorem to this setti...

We consider two-dimensional marked point processes which are Gibbsian with a two-body-potential 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 Mermin-Wagner-Dobrushin-Shlosman 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 Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-11-01

Source:

http://arxiv.org/pdf/math/0407216v1.pdf

http://arxiv.org/pdf/math/0407216v1.pdf Minimize

Document Type:

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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Title:

Translation-Invariance of Two-Dimensional Gibbsian Systems of Particles with Internal Degrees of Freedom, preprint, 2006. Available online from http://www. arxiv.org/abs/math.PR/0603140

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 two-dimensional 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 two-dimensional 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, Mermin-Wagner theorem, translation, hard core, singularity, Widom Rowlinson model, Potts model, percolation. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-11-06

Source:

http://arxiv.org/pdf/math/0603140v4.pdf

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Document Type:

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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Title:

Translation-Invariance of Two-Dimensional Gibbsian Systems of Particles with Internal Degrees of Freedom, preprint, 2006. Available online from http://www. arxiv.org/abs/math.PR/0603140

Description:

The conservation of translation as a symmetry in two-dimensional systems with interaction is a classical subject of statistical mechanics. Here we establish such a result for Gibbsian systems of marked particles with two-body interaction, where the interesting cases of singular, hard-core and discontinuous interaction are included. We start with...

The conservation of translation as a symmetry in two-dimensional systems with interaction is a classical subject of statistical mechanics. Here we establish such a result for Gibbsian systems of marked particles with two-body interaction, where the interesting cases of singular, hard-core 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, Mermin-Wagner theorem, translation, hard-core potential, singular potential, Widom Rowlinson potential Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-11-06

Source:

http://arxiv.org/pdf/math/0603140v2.pdf

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Document Type:

text

Language:

en

Subjects:

percolation

percolation Minimize

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

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Title:

degrees of freedom

Description:

Gibbsian systems of particles with internal

Gibbsian systems of particles with internal Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-11-05

Source:

http://arxiv.org/pdf/math/0603140v1.pdf

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Document Type:

text

Language:

en

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Title:

. Stochastic

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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 Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-11-27

Source:

http://arxiv.org/pdf/0908.1551v1.pdf

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Document Type:

text

Language:

en

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Title:

degrees of freedom

Description:

Gibbsian systems of particles with internal

Gibbsian systems of particles with internal Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-11-06

Source:

http://arxiv.org/pdf/math/0603140v3.pdf

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Document Type:

text

Language:

en

Subjects:

Key words ; Gibbsian point processes ; Mermin-Wagner theorem ; translation ; hard core ; singularity ; Widom Rowlinson potential ; Potts model ; percolation

Key words ; Gibbsian point processes ; Mermin-Wagner theorem ; translation ; hard core ; singularity ; Widom Rowlinson potential ; Potts model ; percolation Minimize

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Title:

Translation-Invariance of Two-Dimensional Gibbsian Systems of Particles with Internal Degrees of Freedom, preprint, 2006. Available online from http://www. arxiv.org/abs/math.PR/0603140

Description:

The conservation of translation as a symmetry in two-dimensional systems with interaction is a classical subject of statistical mechanics. Here we establish such a result for Gibbsian particle systems with two-body interaction, where the interesting cases of singular, hard-core and discontinuous interaction are included. We start with the specia...

The conservation of translation as a symmetry in two-dimensional systems with interaction is a classical subject of statistical mechanics. Here we establish such a result for Gibbsian particle systems with two-body interaction, where the interesting cases of singular, hard-core 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, Mermin-Wagner theorem, translation, hard-core potential, singular potential, pure hard core repulsion Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-12-04

Source:

http://arxiv.org/pdf/0706.3637v1.pdf

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Document Type:

text

Language:

en

Subjects:

percolation

percolation Minimize

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Title:

Proof of Aldous’ spectral gap conjecture

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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. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-11-27

Source:

http://arxiv.org/pdf/0906.1238v4.pdf

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Document Type:

text

Language:

en

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Title:

Percolation of arbitrary words in one dimension

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Description:

We consider a type of long-range 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 long-range 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 Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-11-26

Source:

http://arxiv.org/pdf/0807.1676v1.pdf

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Document Type:

text

Language:

en

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Title:

Percolation of arbitrary words in one dimension

Author:

Description:

We consider a type of long-range 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 long-range 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 Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-01-29

Source:

http://www.math.ucla.edu/~tml/grimmett6.pdf

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Document Type:

text

Language:

en

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