Related papers: Concentration and mean field approximation results…
We establish central limit theorems for a large class of supercritical branching Markov processes in infinite dimension with spatially dependent and non-necessarily local branching mechanisms. This result relies on a fourth moment…
We observe that the technique of Markov contraction can be used to establish measure concentration for a broad class of non-contracting chains. In particular, geometric ergodicity provides a simple and versatile framework. This leads to a…
Transformer-based models have demonstrated exceptional performance across diverse domains, becoming the state-of-the-art solution for addressing sequential machine learning problems. Even though we have a general understanding of the…
We study a simple random process in which vertices of a connected graph reach consensus through pairwise interactions. We compute outcome probabilities, which do not depend on the graph structure, and consider the expected time until a…
In this paper we consider the problem of computing the stationary distribution of nearly completely decomposable Markov processes, a well-established area in the classical theory of Markov processes with broad applications in the design,…
Theta graphs are important geometric graphs that have many applications, including wireless networking, motion planning, real-time animation, and minimum-spanning tree construction. We give closed form expressions for the average degree of…
An instance of the maximum mixed graph orientation problem consists of a mixed graph and a collection of source-target vertex pairs. The objective is to orient the undirected edges of the graph so as to maximize the number of pairs that…
We analyze a class of distributed quantized consen- sus algorithms for arbitrary networks. In the initial setting, each node in the network has an integer value. Nodes exchange their current estimate of the mean value in the network, and…
In causal inference on directed acyclic graphs, the orientation of edges is in general only recovered up to Markov equivalence classes. We study Markov equivalence classes of uniformly random directed acyclic graphs. Using a tower…
We analyze the threshold network model in which a pair of vertices with random weights are connected by an edge when the summation of the weights exceeds a threshold. We prove some convergence theorems and central limit theorems on the…
In this paper we introduce a class of Markov models, termed best-effort networks, designed to capture performance indices such as mean transfer times in data networks with best-effort service. We introduce the so-called min bandwidth…
We investigate systems of interacting stochastic differential equations with two kinds of heterogeneity: one originating from different weights of the linkages, and one concerning their asymptotic relevance when the system becomes large. To…
We consider large systems of particles interacting through rough but bounded interaction kernels. We are able to control the relative entropy between the $N$-particle distribution and the expected limit which solves the corresponding Vlasov…
We study non-stationary averaging processes, where each term of a sequence is a weighted average of previous terms, namely $a_{n+1} = \sum_{j=1}^n p_n(j) a_j$. Our results extend classical theory in two distinct regimes. First, we prove a…
In this paper we consider a simple virus infection spread model on a finite population of $n$ agents connected by some neighborhood structure. Given a graph $G$ on $n$ vertices, we begin with some fixed number of initial infected vertices.…
We consider a decentralized convex unconstrained optimization problem, where the cost function can be decomposed into a sum of strongly convex and smooth functions, associated with individual agents, interacting over a static or…
Mean field approximation is a powerful technique to study the performance of large stochastic systems represented as $n$ interacting objects. Applications include load balancing models, epidemic spreading, cache replacement policies, or…
We give a generalization to a continuous setting of the classic Markov chain tree Theorem. In particular, we consider an irreducible diffusion process on a metric graph. The unique invariant measure has an atomic component on the vertices…
We study normal approximations for a class of discrete-time occupancy processes, namely, Markov chains with transition kernels of product Bernoulli form. This class encompasses numerous models which appear in the complex networks…
We study the asymptotic properties, in the weak sense, of regenerative processes and Markov renewal processes. For the latter, we derive both renewal-type results, also concerning the related counting process, and ergodic-type ones,…