Related papers: Mixing time trichotomy in regenerating dynamic dig…
Temporal graphs (in which edges are active at specified times) are of particular relevance for spreading processes on graphs, e.g.~the spread of disease or dissemination of information. Motivated by real-world applications, modification of…
We present analytical expressions for the time-dependent and stationary probability distributions corresponding to a stochastically perturbed one-dimensional flow with critical points, in two physically relevant situations: delayed…
We present exact results, as well as some illustrative Monte Carlo simulations, concerning a stochastic network with weighted connections in which the fraction of nodes that are dynamically synchronized is a parameter. This allows one to…
It is a fact simple to establish that the mixing time of the simple random walk on a d-regular graph $G_n$ with n vertices is asymptotically bounded from below by $d/ ((d-2)\log (d-1))\log n$. Such a bound is obtained by comparing the walk…
We consider three kinds of discrete-time arrival processes: transient, intermediate and recurrent, characterized by a finite, possibly finite and infinite number of events, respectively. In this context, we study renewal processes which are…
A periodic temporal graph, in its simplest form, is a graph in which every edge appears exactly once in the first $\Delta$ time steps, and then it reappears recurrently every $\Delta$ time steps, where $\Delta$ is a given period length.…
We consider dynamical percolation on the $d$-dimensional discrete torus of side length $n$, $\mathbb{Z}_n^d$, where each edge refreshes its status at rate $\mu=\mu_n\le 1/2$ to be open with probability $p$. We study random walk on the…
We consider Lagrangian systems in the limit of infinitely many particles. It is shown that the corresponding discrete action functionals Gamma-converge to a continuum action functional acting on probability measures of particle…
We study the condensation phenomenon in a zero range process on scale-free networks. We show that the stationary state property depends only on the degree distribution of underlying networks. The model displays a stationary state phase…
We investigate reflected random walks in the quarter plane, with particular emphasis on the time spent along the reflection boundary axes. Assuming the drift of the random walk lies within the cone, the local time converges -- without the…
We use computer simulations to study the relaxation dynamics of a model for oil-in-water microemulsion droplets linked with telechelic polymers. This system exhibits both gel and glass phases and we show that the competition between these…
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…
We study several lattice random walk models with stochastic resetting to previously visited sites which exhibit a phase transition between an anomalous diffusive regime and a localization regime where diffusion is suppressed. The localized…
A well-known conjecture in computer science and statistical physics is that Glauber dynamics on the set of $k$-colorings of a graph $G$ on $n$ vertices with maximum degree $\Delta$ is rapidly mixing for $k\ge\Delta+2$. In FOCS 1999, Vigoda…
We study biased random walks on dynamical percolation on $\mathbb{Z}^d$. We establish a law of large numbers and an invariance principle for the random walk using regeneration times. Moreover, we verify that the Einstein relation holds, and…
We consider the zero-range process with arbitrary bounded monotone rates on the complete graph, in the regime where the number of sites diverges while the density of particles per site converges. We determine the asymptotics of the mixing…
Motivated by the study of reversal behaviour of myxobacteria, in this article we are interested in a kinetic model for reversal dynamics, in which particles with directions close to be opposite undergo binary collision resulting in…
Graph matching---aligning a pair of graphs to minimize their edge disagreements---has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and…
Recently it was shown that the transitive closure of a directed graph can be updated using first-order formulas after insertions and deletions of single edges in the dynamic descriptive complexity framework by Dong, Su, and Topor, and…
We consider a class of multi-particle reinforced interacting random walks. In this model, there are some (finite or infinite) particles performing random walks on a given (finite or infinite) connected graph, so that each particle has…