Related papers: A limit theorem for diffusions on graphs with vari…
The present paper is concerned with diffusion processes running on tubular domains with conditions on nonreaching the boundary, respectively, reflecting at the boundary, and corresponding processes in the limit where the thin tubular…
We consider diffusion processes on metric graphs with semipermeable sticky membranes in each vertex. We prove that the process is governed by a Feller semigroup and find its asymptotic behavior as diffusion's speed increases to infinity…
A finite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered…
We present two limit theorems, a mean ergodic and a central limit theorem, for a specific class of one-dimensional diffusion processes that depend on a small-scale parameter $\varepsilon$ and converge weakly to a homogenized diffusion…
We consider the edge-triangle model, a two-parameter family of exponential random graphs in which dependence between edges is introduced through triangles. In the so-called replica symmetric regime, the limiting free energy exists together…
This paper proves limit theorems for the number of monochromatic edges in uniform random colorings of general random graphs. These can be seen as generalizations of the birthday problem (what is the chance that there are two friends with…
The bifurcation theory of ordinary differential equations (ODEs), and its application to deterministic population models, are by now well established. In this article, we begin to develop a complementary theory for diffusion-like…
For a given homogeneous Poisson point process in $\mathbb{R}^d$ two points are connected by an edge if their distance is bounded by a prescribed distance parameter. The behaviour of the resulting random graph, the Gilbert graph or random…
We consider singularly perturbed convection-diffusion equations on one-dimensional networks (metric graphs) as well as the transport problems arising in the vanishing diffusion limit. Suitable coupling condition at inner vertices are…
We investigate fast diffusions on finite directed graphs. We prove results in a way dual to presented in Bobrowski, A. Ann. Henri Poincar\'e (2012) 13(6): 1501-1510 and Bobrowski, A., Morawska, K. DCDS-B (2012), 17(7): 2313-2327, and obtain…
We prove that for any weakly convergent sequence of finite graphs with bounded vertex degrees, there exists a topological limit graphing.
We consider a positive recurrent one-dimensional diffusion process with continuous coefficients and we establish stable central limit theorems for a certain type of additive functionals of this diffusion. In other words we find some…
We show that if a sequence of dense graphs has the property that for every fixed graph F, the density of copies of F in these graphs tends to a limit, then there is a natural ``limit object'', namely a symmetric measurable 2-variable…
We prove limit theorems for systems of interacting diffusions on sparse graphs. For example, we deduce a hydrodynamic limit and the propagation of chaos property for the stochastic Kuramoto model with interactions determined by…
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 get central limit type theorems for the total number of edges in the generalized random graphs with random vertex weights under different moment conditions on distributions of the weights.
This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…
We give sufficient conditions under which a random graph with a specified degree sequence is symmetric or asymmetric. In the case of bounded degree sequences, our characterisation captures the phase transition of the symmetry of the random…
The modeling of diffusion processes on graphs is the basis for many network science and machine learning approaches. Entropic measures of network-based diffusion have recently been employed to investigate the reversibility of these…
The paper presents a generalization of the local limit theorem on the convergence of inhomogeneous Markov chains to the diffusion limit for the case where the corresponding process coefficients satisfy weak regularity conditions and…