相关论文: Asymptotic geometry of discrete interlaced pattern…
We consider any fixed $d\in\mathbb{Z}_{>0}$ number of second class particles in the asymmetric simple exclusion process (ASEP), constructed via a basic coupling of two ASEPs. We give the joint distribution of the positions of the second…
We consider the random deposition of objects of variable width and height over a line. The successive additions of these structures create a random interface. We focus on the regime of heavy tailed distributions of the structure width. When…
Recently, we proposed a self-propelled particle model with competing alignment interactions: nearby particles tend to align their velocities whereas they anti-align their direction of motion with particles which are further away [R.…
This article is the first of two in which we develop a geometric framework for analysing silent and anisotropic big bang singularities. The results of the present article concern the asymptotic behaviour of solutions to linear systems of…
We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…
In this paper we consider a class of probability distributions on the six-vertex model from statistical mechanics, which originate from the higher spin vertex models of https://arxiv.org/abs/1601.05770. We define operators, inspired by the…
In this note we study a natural measure on plane partitions giving rise to a certain discrete-time Muttalib-Borodin process (MBP): each time-slice is a discrete version of a Muttalib-Borodin ensemble (MBE). The process is determinantal with…
Assemblies of anisotropic particles commonly appear in studies of active many-body systems. However, in two dimensions, the geometric ramifications of the finite density of such objects are not entirely understood. To fully characterize…
A continuation of the joint work by Vadim Gorin and the author, J. Funct. Anal. 270 (2016), 375-418; arXiv:1504.06832. The extended Gelfand-Tsetlin graph, introduced in that paper, is a novel combinatorial object. Its q-boundary is formed…
We consider a system of parallel straight edge dislocations and we analyse its asymptotic behaviour in the limit of many dislocations. The dislocations are represented by points in a plane, and they are arranged in vertical walls; each wall…
We consider diffusion on discrete measure spaces as encoded by Markovian semigroups arising from weighted graphs. We study whether the graph is uniquely determined if the diffusion is given up to order isomorphism. If the graph is recurrent…
A theory of structure is formulated for systems of many structureless classical particles with stable local interactions in Euclidean space. Such systems are shown to have their structure in thermodynamic equilibrium determined exactly by a…
We prove an asymptotic crystallization result in two dimensions for a class of nonlocal particle systems. To be precise, we consider the best approximation with respect to the 2-Wasserstein metric of a given absolutely continuous…
The crystalline solids with lack of orientational ordering of anisotropic particles serve the purpose of studying the disordered systems with many fundamental applications in contemporary research. Despite the orientational disorder,…
We investigate a discrete model consisting of self-propelled particles that obey simple interaction rules. We show that this model can self-organize and exhibit coherent localized solutions in one- and in two-dimensions.In one-dimension,…
We study the normal matrix model, also known as the two-dimensional one-component plasma at a specific temperature, with merging singularity. As the number $n$ of particles tends to infinity we obtain the limiting local correlation kernel…
In this note we present new examples of determinantal point processes with infinitely many particles. The particles live on the half-lattice {1,2,...} or on the open half-line (0,+\infty). The main result is the computation of the…
Connectedness percolation phenomena in two-dimensional packings of elongated particles (discorectangles) were studied numerically. The packings were produced using random sequential adsorption (RSA) off-lattice model with preferential…
We study the size-topology relations in random packings of dry adhesive polydisperse microspheres with Gaussian and lognormal size distributions through a geometric tessellation. We find that the dependence of the neighbour number on the…
We study the behaviour of interacting self-propelled particles, whose self-propulsion speed decreases with their local density. By combining direct simulations of the microscopic model with an analysis of the hydrodynamic equations obtained…