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We consider - in uniformly strictly convex potential regime - two versions of random gradient models with disorder. In model (A) the interface feels a bulk term of random fields while in model (B) the disorder enters though the potential…

Probability · Mathematics 2014-09-16 Codina Cotar , Christof Külske

We consider statistical mechanics models of continuous spins in a disordered environment. These models have a natural interpretation as effective interface models. It is well known that without disorder there are no interface Gibbs measures…

Probability · Mathematics 2009-09-29 Aernout C. D. van Enter , Christof Külske

Gibbsian line ensembles are families of Brownian lines arising in many natural contexts such as the level curves of three dimensional Ising interfaces, the solid-on-solid model, multi-layered polynuclear growth etc. An important example is…

Probability · Mathematics 2023-10-11 Mriganka Basu Roy Chowdhury , Pietro Caputo , Shirshendu Ganguly

We prove that, unless P=NP, there is no polynomial-time algorithm to approximate within some multiplicative constant the average size of an independent set in graphs of maximum degree 6. This is a special case of a more general result for…

Computational Complexity · Computer Science 2021-07-20 Andreas Galanis , Daniel Stefankovic , Eric Vigoda

We study the hard-core model defined on independent sets, where each independent set I in a graph G is weighted proportionally to $\lambda^{|I|}$, for a positive real parameter $\lambda$. For large $\lambda$, computing the partition…

Probability · Mathematics 2011-08-15 Ricardo Restrepo , Jinwoo Shin , Prasad Tetali , Eric Vigoda , Linji Yang

We consider a hard core (HC) model with a countable set $\mathbb{Z}$ of spin values on the Cayley tree. This model is defined by a countable set of parameters $\lambda_{i}>0, i \in \mathbb{Z}\setminus\{0\}$. For all possible values of…

Dynamical Systems · Mathematics 2023-02-22 U. A. Rozikov , F. H. Haydarov

We study the zero-free regions of the partition function of the hard-core model on finite graphs and their implications for the analyticity of the free energy on infinite lattices. Classically, zero-freeness results have been established up…

Statistical Mechanics · Physics 2026-04-06 Yuan Chen , Shuai Shao , Ke Shi

We study a model of spatial random permutations over a discrete set of points. Formally, a permutation $\sigma$ is sampled proportionally to the weight $\exp\{-\alpha \sum_x V(\sigma(x)-x)\},$ where $\alpha>0$ is the temperature and $V$ is…

Probability · Mathematics 2019-04-09 Inés Armendáriz , Pablo A. Ferrari , Nicolás Frevenza

We prove that for every locally stable and tempered pair potential $\phi$ with bounded range, there exists a unique infinite-volume Gibbs point process on $\mathbb{R}^d$ for every activity $\lambda < (e^{L} \hat{C}_{\phi})^{-1}$, where $L$…

Probability · Mathematics 2024-07-02 Samuel Baguley , Andreas Göbel , Marcus Pappik

We study the hard-core model defined on independent sets of an input graph where the independent sets are weighted by a parameter $\lambda>0$. For constant $\Delta$, previous work of Weitz (2006) established an FPTAS for the partition…

Discrete Mathematics · Computer Science 2016-08-30 Charilaos Efthymiou , Thomas P. Hayes , Daniel Stefankovic , Eric Vigoda , Yitong Yin

We consider the soft-core Widom-Rowlinson model for particles with spins and holes, on a Cayley tree of order $d$ (which has $d + 1$ nearest neighbours), depending on repulsion strength $\beta$ between particles of different signs and on an…

Probability · Mathematics 2023-02-14 Sebastian Bergmann , Sascha Kissel , Christof Kuelske

We study the computational complexity of approximately counting the number of independent sets of a graph with maximum degree Delta. More generally, for an input graph G=(V,E) and an activity lambda>0, we are interested in the quantity…

Computational Complexity · Computer Science 2013-08-12 Andreas Galanis , Qi Ge , Daniel Stefankovic , Eric Vigoda , Linji Yang

We study how to establish $\textit{spectral independence}$, a key concept in sampling, without relying on total influence bounds, by applying an $\textit{approximate inverse}$ of the influence matrix. Our method gives constant upper bounds…

Data Structures and Algorithms · Computer Science 2024-04-09 Xiaoyu Chen , Xiongxin Yang , Yitong Yin , Xinyuan Zhang

The hard-core model has as its configurations the independent sets of some graph instance $G$. The probability distribution on independent sets is controlled by a `fugacity' $\lambda>0$, with higher $\lambda$ leading to denser…

Probability · Mathematics 2026-01-14 Mark Jerrum

We aim at understanding for which (complex) values of the potential the pinning partition function vanishes. The pinning model is a Gibbs measure based on discrete renewal processes with power law inter-arrival distributions. We obtain some…

Mathematical Physics · Physics 2022-09-01 Giambattista Giacomin , Rafael L. Greenblatt

We study computational aspects of repulsive Gibbs point processes, which are probabilistic models of interacting particles in a finite-volume region of space. We introduce an approach for reducing a Gibbs point process to the hard-core…

Data Structures and Algorithms · Computer Science 2023-12-15 Tobias Friedrich , Andreas Göbel , Maximilian Katzmann , Martin Krejca , Marcus Pappik

In this paper we investigate generalized Gibbs measure (GGM) for $p$-adic Hard-Core(HC) model with a countable set of spin values on a Cayley tree of order $k\geq 2$. This model is defined by $p$-adic parameters $\lambda_i$, $i\in \mathbb…

Functional Analysis · Mathematics 2022-07-12 U. A. Rozikov , I. A. Sattarov , A. M. Tukhtabaev

The Gibbs measures of a spin system on $Z^d$ with unbounded pair interactions $J_{xy} \sigma (x) \sigma (y)$ are studied. Here $\langle x, y \rangle \in E $, i.e. $x$ and $y$ are neighbors in $Z^d$. The intensities $J_{xy}$ and the spins…

Mathematical Physics · Physics 2010-08-17 Yuri Kondratiev , Yuri Kozitsky , Tanja Pasurek

In this paper we consider a nearest-neighbor $p$-adic hard core (HC) model, with fugacity $\lambda$, on a homogeneous Cayley tree of order $k$ (with $k + 1$ neighbors). We focus on $p$-adic Gibbs measures for the HC model, in particular on…

Mathematical Physics · Physics 2011-07-26 D. Gandolfo , U. A. Rozikov , J. Ruiz

We study a class of Gibbs measures of classical particle spin systems with spin space $S=\mathbb{R}^{m}$ and unbounded pair interaction, living on a metric graph given by a typical realization $\gamma $ of a random point process in…

Mathematical Physics · Physics 2015-06-16 Alexei Daletskii , Yuri Kondratiev , Yuri Kozitsky , Tanja Pasurek