Related papers: A limit theorem for diffusions on graphs with vari…
We prove a general theorem on cutoffs for symmetric exclusion and interchange processes on finite graphs $G_N=(V_N,E_N)$, under the assumption that either the graphs converge geometrically and spectrally to a compact metric measure space,…
In an earlier paper the authors proved that limits of convergent graph sequences can be described by various structures, including certain 2-variable real functions called graphons, random graph models satisfying certain consistency…
We consider limit probabilities of first order properties in random graphs with a given degree sequence. Under mild conditions on the degree sequence, we show that the closure set of limit probabilities is a finite union of closed…
The clearing up of a wave nature of the energy and mass transfer phenomena in classical expressions of the molecular-kinetic theory has allowed to find a quantitative measure of intensity of processes of a thermal conductivity, viscosity…
In this paper we prove Morse index theorems for a big class of constrained variational problems on graphs. Such theorems are useful in various physical and geometric applications. Our formulas compute the difference of Morse indices of two…
Infiltration of diffusing particles from one material to another where the diffusion mechanism is either normal or anomalous is a widely observed phenomena. When the diffusion is anomalous we find interesting behaviors: diffusion may lead…
For a minimal diffusion process on $ (a,b) $, any possible extension of it to a standard process on $ [a,b] $ is characterized by the characteristic measures of excursions away from the boundary points $ a $ and $ b $. The generator of the…
Diffusion processes have been widely used for approximations in the queueing theory. There are different types of diffusion approximations. Among them, we are interested in those obtained through limits of a sequence of models which…
A central limit theorem is established for a sum of random variables belonging to a sequence of random fields. The fields are assumed to have zero mean conditional on the past history and to satisfy certain conditional $\alpha$-mixing…
Graph burning studies how fast a contagion, modeled as a set of fires, spreads in a graph. The burning process takes place in synchronous, discrete rounds. In each round, a fire breaks out at a vertex, and the fire spreads to all vertices…
We consider a sequence of Markov chains weakly convergent to a diffusion. We suppose that a drift term contains a linearly increasing component. The usual parametrix method fails because of this unbounded drift term. We show how to modify…
A matching in a graph is uniquely restricted if no other matching covers exactly the same set of vertices. We establish tight lower bounds on the maximum size of a uniquely restricted matching in terms of order, size, and maximum degree.
We prove a Large Deviations Principle (LDP) for systems of diffusions (particles) interacting through their ranks, when the number of particles tends to infinity. We show that the limiting particle density is given by the unique solution of…
In this article, we study the large-population limit of interacting particle systems posed on weighted random graphs. In that aim, we introduce a general framework for the construction of weighted random graphs, generalizing the concept of…
Consider a family of graphs having a fixed girth and a large size. We give an optimal lower asymptotic bound on the number of even cycles of any constant length, as the order of the graphs tends to infinity.
In this paper, we study the diffusive limit of the steady state radiative heat transfer system for non-homogeneous Dirichlet boundary conditions in a bounded domain with flat boundaries. A composite approximate solution is constructed using…
The theory of graphons comes with a natural sampling procedure, which results in an inhomogeneous variant of the Erd\H{o}s--R\'enyi random graph, called $W$-random graphs. We prove, via the method of moments, a limit theorem for the number…
Consider a stationary Poisson point process in $\mathbb{R}^d$ and connect any two points whenever their distance is less than or equal to a prescribed distance parameter. This construction gives rise to the well known random geometric…
We study a variant of the chip-firing game called the diffusion game. In the diffusion game, we begin with some integer labelling of the vertices of a graph, interpreted as a number of chips on each vertex, and then for each subsequent step…
We present a new theoretical framework for Diffusion Limited Aggregation and associated Dielectric Breakdown Models in two dimensions. Key steps are understanding how these models interrelate when the ultra-violet cut-off strategy is…