Related papers: Interacting diffusions on sparse graphs: hydrodyna…
Consider a set of $n$ vertices, where each vertex has a location in $\mathbb{R}^d$ that is sampled uniformly from the unit cube in $\mathbb{R}^d$, and a weight associated to it. Construct a random graph by placing edges independently for…
Motivated by limits of critical inhomogeneous random graphs, we construct a family of sequences of measured metric spaces that we call continuous multiplicative graphs, that are expected to be the universal limit of graphs related to the…
In this article, local limit theorems for sequences of simple random walks on graphs are established. The results formulated are motivated by a variety of random graph models, and explanations are provided as to how they apply to…
We construct a nearest-neighbour interacting particle system of exclusion type, which illustrates a transition from slow to fast diffusion. More precisely, the hydrodynamic limit of this microscopic system in the diffusive space-time…
We study the breakdown of diffusive hydrodynamics in holographic systems dual to neutral dilatonic black holes with extremal near horizon geometries conformal to AdS$_2\times\,$R$^2$. We find that at low temperatures by tuning the effective…
Let $P(n,m)$ be a graph chosen uniformly at random from the class of all planar graphs on vertex set $\left\{1, \ldots, n\right\}$ with $m=m(n)$ edges. We determine the (Benjamini-Schramm) local weak limit of $P(n,m)$ in the sparse regime…
This paper develops a theory of propagation of chaos for a system of weakly interacting particles whose terminal configuration is fixed as opposed to the initial configuration as customary. Such systems are modeled by backward stochastic…
We study a sequential system of interacting diffusions in which particle $i$ interacts only with its predecessors through the empirical measure $\mu_t^{i-1}$, yielding a directed, non-exchangeable mean-field approximation of a…
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…
We consider hydrodynamic scaling limits for a class of reversible interacting particle systems, which includes the symmetric simple exclusion process and certain zero-range processes. We study a (non-quadratic) microscopic action functional…
A new approach to the modeling of nonfree particle diffusion is presented. The approach uses a general setup based on geometric graphs (networks of curves), which means that particle diffusion in anything from arrays of barriers and pore…
We make the first steps towards generalizing the theory of stochastic block models, in the sparse regime, towards a model where the discrete community structure is replaced by an underlying geometry. We consider a geometric random graph…
We study numerically the correlations and the distribution of intervals between successive zeros in the fluctuating geometry of stochastic interfaces, described by the Edwards-Wilkinson equation. For equilibrium states we find that the…
This paper is devoted to an interacting particle system that provides probabilistic interpretation of the wave equation on graphs. A Feynman-Kac-type formula is established, connecting the expectation of the process with the wave equation…
In this paper, we study diffusion social learning over weakly-connected graphs. We show that the asymmetric flow of information hinders the learning abilities of certain agents regardless of their local observations. Under some…
Constraints can affect dramatically the behavior of diffusion processes. Recently, we analyzed a natural and a technological system and reported that they perform diffusion-like discrete steps displaying a peculiar constraint, whereby the…
A Kawasaki dynamics in continuum is a dynamics of an infinite system of interacting particles in $\mathbb R^d$ which randomly hop over the space. In this paper, we deal with an equilibrium Kawasaki dynamics which has a Gibbs measure $\mu$…
We prove the existence of weak solutions of a class of multi-species cross-diffusion systems as well as the propagation of chaos result by means of nonlocal approximation of the nonlinear diffusion terms, coupling methods and compactness…
This paper studies the derivation of the quadratic porous medium equation and a class of cross-diffusion systems from nonlocal interactions. We prove convergence of solutions of a nonlocal interaction equation, resp. system, to solutions of…
We consider dynamical graphs, namely graphs that evolve over time, and investigate a notion of local weak convergence that extends naturally the usual Benjamini-Schramm local weak convergence for static graphs. One of the well-known results…