相关论文: Modeles avec particules dures, animaux diriges et …

In this paper, we revisit the enumeration of directed animals using gas models. We show that there exists a natural construction of random directed animals on any directed graph together with a particle system that explains at the level of…

Here we introduce simple structures for the analysis of complex hypergraphs, hypergraph animals. These structures are designed to describe the local node neighbourhoods of nodes in hypergraphs. We establish their relationships to lattice…

We introduce new combinatorial (bijective) methods that enable us to compute the average value of three parameters of directed animals of a given area, including the site perimeter. Our results cover directed animals of any one-line source…

A directed animal is a percolation cluster in the directed site percolation model. The aim of this paper is to exhibit a strong relation between the problem of computing the generating function $\G$ of directed animals on the square…

We present a new method to describe the kinetics of driven lattice gases with particle-particle interactions beyond hard-core exclusions. The method is based on the time-dependent density functional theory for lattice systems and allows one…

A simple lattice gas model in one dimension is constructed in which each site can be occupied by at most one particle of any one of $D$ species. Particles interact with a randomly drawn nearest neighbor interaction. This model is capable of…

We construct a simple multicomponent lattice gas model in one dimension in which each site can either be empty or occupied by at most one particle of any one of $D$ species. Particles interact with a nearest neighbor interaction which…

We derive exact relations for $N$ spin-1/2 fermions with zero-range or short-range interactions, in continuous space or on a lattice, in $2D$ or in $3D$, in any external potential. Some of them generalize known relations between energy,…

This article introduces a new, simple solvable lattice for directed animals: the directed king's lattice, or square lattice with next nearest neighbor bonds and preferred directions {W, NW, N, NE, E}. We show that the directed animals in…

We consider the application of deep generative models in propagating uncertainty through complex physical systems. Specifically, we put forth an implicit variational inference formulation that constrains the generative model output to…

We reassess the relation between classical lattice dimer models and the continuum elastic description of a lattice of fluctuating polymers. In the absence of randomness we determine the density and line tension of the polymers in terms of…

We discuss stationary aspects of a set of driven lattice gases in which hard-core particles with spatial extent, covering more than one lattice site, diffuse and reconstruct in one dimension under nearest-neighbor interactions. As in the…

The equilibrium statistical mechanics of one-dimensional lattice gases with interactions of arbitrary range and shape between first-neighbor atoms is solved exactly on the basis of statistically interacting vacancy particles. Two sets of…

Statistical physics models with hard constraints, such as the discrete hard-core gas model (random independent sets in a graph), are inherently combinatorial and present the discrete mathematician with a relatively comfortable setting for…

The discrete power function on the hexagonal lattice proposed by Bobenko et al is considered, whose defining equations consist of three cross-ratio equations and a similarity constraint. We show that the defining equations are derived from…

Nonlinear relationships between covariates and a response variable of interest are frequently encountered in animal science research. Within statistical models, these nonlinear effects have, traditionally, been handled using a range of…

Stacked directed animals and multi-directed animals are two lattice models defined by Bousquet-M\'{e}lou and Rechnitzer in 2002. The original definitions of those models involve heaps of pieces, i.e., some geometric representation of…

In this work a theory is developed for unifying large classes of nonlinear discrete-time dynamical systems obeying a superposition of a weighted maximum or minimum type. The state vectors and input-output signals evolve on nonlinear spaces…

In this article we tackle the combinatorics of coloured hard-dimer objects. This is achieved by identifying coloured hard-dimer configurations with a certain class of rooted trees that allow for an algebraic treatment in terms of…

We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…