Related papers: Simultaneous Cutoff on the Multitype Configuration…

This work describes probabilistic methods for utilizing random spanning trees generated via a random walk process. Goyal et al. showed that the union of random spanning trees approximates the expansion of every cut of a graph. First, we…

We study numerically the behavior of continuous-time quantum walks over networks which are topologically equivalent to square lattices. On short time scales, when placing the initial excitation at a corner of the network, we observe a fast,…

Random walks find applications in many areas of science and are the heart of essential network analytic tools. When defined on temporal networks, even basic random walk models may exhibit a rich spectrum of behaviours, due to the…

We define the probability structure of a continuous-time time-homogeneous Markov jump process, on a finite graph, that represents the continuous-time counterpart of the so-called Ruelle-Bowen discrete-time random walk. It constitutes the…

The total variation distance is a core statistical distance between probability measures that satisfies the metric axioms, with value always falling in $[0,1]$. This distance plays a fundamental role in machine learning and signal…

This work analyzes fractional continuous-time random walks on two-layer multiplexes. A node-centric dynamics is used, in which it is assumed a Poisson distribution of a walker to become active, while a jump to one of its neighbors depends…

We consider the simple random walk on random graphs generated by discrete point processes. This random graph has a random subset of a cubic lattice as the vertices and lines between any consecutive vertices on lines parallel to each…

In this paper we study a random graph with $N$ nodes, where node $j$ has degree $D_j$ and $\{D_j\}_{j=1}^N$ are i.i.d. with $\prob(D_j\leq x)=F(x)$. We assume that $1-F(x)\leq c x^{-\tau+1}$ for some $\tau>3$ and some constant $c>0$. This…

Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…

We consider a mortal random walker on a family of hierarchical graphs in the presence of some trap sites. The configuration comprising the graph, the starting point of the walk, and the locations of the trap sites is taken to be exactly…

We extend stochastic network optimization theory to treat networks with arbitrary sample paths for arrivals, channels, and mobility. The network can experience unexpected link or node failures, traffic bursts, and topology changes, and…

Consider longitudinal networks whose edges turn on and off according to a discrete-time Markov chain with exponential-family transition probabilities. We characterize when their joint distributions are also exponential families with the…

The configuration model is a sequence of random graphs constructed such that in the large network limit the degree distribution converges to a pre-specified probability distribution. The component structure of such random graphs can be…

We study multi-marginal optimal transport problems from a probabilistic graphical model perspective. We point out an elegant connection between the two when the underlying cost for optimal transport allows a graph structure. In particular,…

Consider the following asynchronous, opportunistic communication model over a graph $G$: in each round, one edge is activated uniformly and independently at random and (only) its two endpoints can exchange messages and perform local…

The field of complex networks studies a wide variety of interacting systems by representing them as networks. To understand their properties and mutual relations, the randomisation of network connections is a commonly used tool. However,…

Degree distribution, or equivalently called degree sequence, has been commonly used to be one of most significant measures for studying a large number of complex networks with which some well-known results have been obtained. By contrast,…

We prove that the mixing time of driven-dissipative activated random walk on an interval of length $n$ with uniform or central driving exhibits cutoff at $n$ times the critical density for activated random walk on the integers. The proof…

Models for generating simple graphs are important in the study of real-world complex networks. A well established example of such a model is the erased configuration model, where each node receives a number of half-edges that are connected…

Let $X$ be a continuous time random walk on a weighted graph. Given the on-diagonal upper bounds of transition probabilities at two vertices $x_1$ and $x_2$, we use an adapted metric initiated by Davies, and obtain Gaussian upper estimates…