Related papers: Replica-mean-field limit of continuous-time fragme…
In this paper we consider piecewise affine differential equations modeling gene networks. We work with arbitrary decay rates, and under a local hypothesis expressed as an alignment condition of successive focal points. The interaction graph…
Empirical contact networks or interaction networks demonstrate peculiar characteristics stemming from the fundamental social, psychological, physical mechanisms governing human interactions. Although these mechanisms are complex, we test…
We develop a unified theory that encompasses the macroscopic dynamics of recurrent interactions of binary units within arbitrary network architectures. Using the martingale theory, our mathematical analysis provides a complete description…
In many biological systems, motile agents exhibit random motion with short-term directional persistence, together with crowding effects arising from spatial exclusion. We formulate and study a class of lattice-based models for multiple…
Continuous-time Bayesian networks is a natural structured representation language for multicomponent stochastic processes that evolve continuously over time. Despite the compact representation, inference in such models is intractable even…
Complex networks represent the natural backbone to study epidemic processes in populations of interacting individuals. Such a modeling framework, however, is naturally limited to pairwise interactions, making it less suitable to properly…
Higher-order interactions play an important role in complex contagion processes. Mean-field approximations have been used to characterize the onset of spreading in the presence of group interactions. However, individual-based mean-field…
The process by which one may take a discrete model of a biophysical process and construct a continuous model based on it is of mathematical interest as well as being of practical use. In this paper, we first study the singular limit of a…
We consider an interacting particle system, which generalizes the classical totally asymmetric simple exclusion process (TASEP), in that each site can contain up to a fixed finite number of particles, and the particle movement is governed…
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…
This study considers the Merton model with temporal correlation. We show the Merton model becomes Poisson process with the log-normal distributed intensity function in the limit. We discuss the relation between this model and Hawkes…
We obtain quenched hitting distributions to be compound Poissonian for a certain class of random dynamical systems. The theory is general and designed to accommodate non-uniformly expanding behavior and targets that do not overlap much with…
In this work, we consider one-dimensional particles interacting in mean-field type through a bounded kernel. In addition, when particles hit some barrier (say zero), they are removed from the system. This absorption of particles is…
A popular approach to model interactions is to represent them as a network with nodes being the agents and the interactions being the edges. Interactions are often timestamped, which leads to having timestamped edges. Many real-world…
In this paper we study the Poisson Hypothesis, which is a device to analyze approximately the behavior of large queueing networks. We prove it in some simple limiting cases. We show in particular that the corresponding dynamical system,…
Random arrangements of points in the plane, interacting only through a simple hard core exclusion, are considered. An intensity parameter controls the average density of arrangements, in analogy with the Poisson point process. It is proved…
Consider a stationary renewal point process on the real line and divide each of the segments it defines in a proportion given by \iid realisations of a fixed distribution $G$ supported by [0,1]. We ask ourselves for which interpoint…
We construct an infinitely exchangeable process on the set $\cate$ of subsets of the power set of the natural numbers $\mathbb{N}$ via a Poisson point process with mean measure $\Lambda$ on the power set of $\mathbb{N}$. Each $E\in\cate$…
A theory of relative species abundance on sparsely-connected networks is presented by investigating the replicator dynamics with symmetric interactions. Sparseness of a network involves difficulty in analyzing the fixed points of the…
We introduce a model of interacting Random Walk, whose hopping amplitude depends on the number of walkers/particles on the link. The mesoscopic counterpart of such a microscopic dynamics is a diffusing system whose diffusivity depends on…