Related papers: Stochastic Sandpile Model: exact sampling and comp…
We consider a random walk on a discrete connected graph having some infinite branches plus finitely many vertices with finite degrees. We find the generator of a strong stationary dual in the sense of Fill, and use it to find some…
We develop two statistical models for space-time abundance data based on a stochastic underlying continuous individual movement. In contrast to current models for abundance in statistical ecology, our models exploit the explicit connection…
A realistic continuous-time dynamics for fiber bundles is introduced and studied both analytically and numerically. The equation of motion reproduces known stationary-state results in the deterministic limit while the system under…
We present simulations of static model sandpiles in two dimensions (2D) and focus on the stress distribution in such arrays made of discrete particles. We use the simplest possible model, i.e. spherical particles with a linear spring and a…
In this paper, we propose Continuous Graph Flow, a generative continuous flow based method that aims to model complex distributions of graph-structured data. Once learned, the model can be applied to an arbitrary graph, defining a…
We study a directed stochastic sandpile model of Self-Organized Criticality, which exhibits recurrent, multiple topplings, putting it in a separate universality class from the exactly solved model of Dhar and Ramaswamy. We show that in the…
Understanding the behavior of stochastic gradient methods is a central problem in modern machine learning. Recent work has highlighted diagonal linear networks as a simplified yet expressive setting for analyzing the optimization and…
An analytical approach to network dynamics is used to show that when agents copy their state randomly the network arrives to a stationary status in which the distribution of states is independent of the agents degree. The effects of network…
We consider a basic model of a dynamical distribution network, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and…
We propose a method to sample stationary properties of solutions of stochastic differential equations, which is accurate and efficient if there are rarely visited regions or rare transitions between distinct regions of the state space. The…
We consider an infinite locally finite system (configuration) $\gamma$ of particles distributed over a Euclidean space $X$. Each particle located at $x\in X$ carries an internal parameter (mark, or ``spin'') $\sigma_{x}\in S=\mathbb{R}.$…
In this paper we study the statistical properties of a reversible cellular automaton in two out-of-equilibrium settings. In the first part we consider two instances of the initial value problem, corresponding to the inhomogeneous quench and…
A major difficulty in studying the Bak-Sneppen model is in effectively comparing it with well-understood models. This stems from the use of two geometries: complete graph geometry to locate the global fitness minimizer, and graph geometry…
A stationary spatial model is an idealization and we expect that the true dependence structures of physical phenomena are spatially varying, but how should we handle this non-stationarity in practice? We study the challenges involved in…
Starting from a stochastic individual-based description of an SIS epidemic spreading on a random network, we study the dynamics when the size $n$ of the network tends to infinity. We recover in the limit an infinite-dimensional…
The empirical relation between density and velocity of pedestrian movement is not completely analyzed, particularly with regard to the `microscopic' causes which determine the relation at medium and high densities. The simplest system for…
The existence and uniqueness of the stationary distribution of the numerical solution generated by the stochastic theta method is studied. When the parameter theta takes different values, the requirements on the drift and diffusion…
Over the past few years, research on deep graph learning has shifted from static graphs to temporal graphs in response to real-world complex systems that exhibit dynamic behaviors. In practice, temporal graphs are formalized as an ordered…
We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also…
Much recent research activity has been devoted to empirical study and theoretical models of complex networks (random graphs) with three qualitative features: power-law degree distribution, local clustering of edges, and small diameter. We…