Related papers: Random walks on dense graphs and graphons
This paper studies the on- and off-diagonal upper estimate and the two-sided transition probability estimate of random walks on weighted graphs.
We introduce a discrete-time random walk model on a one-dimensional lattice with a nonconstant sojourn time and prove that the discrete density converges to a solution of a continuum diffusion equation. Our random walk model is not…
A scaling limit for the simple random walk on the largest connected component of the Erdos-Renyi random graph in the critical window is deduced. The limiting diffusion is constructed using resistance form techniques, and is shown to satisfy…
We consider a continuous-time random walk which is defined as an interpolation of a random walk on a point process on the real line. The distances between neighboring points of the point process are i.i.d. random variables in the normal…
We consider discrete and continuous representations of a thermodynamic process in which a random walker (e.g. a molecular motor on a molecular track) uses a periodically pumped energy (work) to pass $N$ sites and move energetically downhill…
Random walks are studied on disordered cellular networks in 2-and 3-dimensional spaces with arbitrary curvature. The coefficients of the evolution equation are calculated in term of the structural properties of the cellular system. The…
We consider a model for random walks on random environments (RWRE) with random subset of the d-dimensional Euclidean lattice as the vertices, and uniform transition probabilities on 2d points (two "coordinate nearest points" in each of the…
This paper investigates the behavior of the Min-Sum message passing scheme to solve systems of linear equations in the Laplacian matrices of graphs and to compute electric flows. Voltage and flow problems involve the minimization of…
A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science.…
We examine diffusion-limited aggregation for a one-dimensional random walk with long jumps. We achieve upper and lower bounds on the growth rate of the aggregate as a function of the number of moments a single step of the walk has. In this…
Random walks are at the heart of many existing deep learning algorithms for graph data. However, such algorithms have many limitations that arise from the use of random walks, e.g., the features resulting from these methods are unable to…
In this paper we derive an analytical expression for the mean load at each node of an arbitrary undirected graph for the uniform multicommodity flow problem under random walk routing. We show the mean load is linearly dependent on the nodal…
Inspired by the study of edge statistics of random band matrices, we investigate random walks on large $d$-dimensional periodic lattices, whose transition matrices are determined by discretized density functions. Under certain moment…
We consider weakly interacting jump processes on time-varying random graphs with dynamically changing multi-color edges. The system consists of a large number of nodes in which the node dynamics depends on the joint empirical distribution…
Consider a network of $n$ single-server queues where tasks arrive independently at each server at rate $\lambda_n$. The servers are connected by a graph that is resampled at rate $\mu_n$ in a way that is symmetric with respect to the…
Random walk has wide applications in many fields, such as machine learning, biology, physics, and chemistry. Random walk can be discrete or continuous in time and space. Asymmetric random walk could be described by drift-diffusion equation.…
In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisson equilibrium with density $\rho \in (0,\infty)$.…
We obtain upper bounds (in most cases, sharp) for the hitting times of random walks on finite undirected graphs expressed as functions of the graph's number of edges. In particular, we show that the maximum hitting time for a simple random…
We analyse the mixing profile of a random walk on a dynamic random permutation, focusing on the regime where the walk evolves much faster than the permutation. Two types of dynamics generated by random transpositions are considered: one…
Simple random walks are a basic staple of the foundation of probability theory and form the building block of many useful and complex stochastic processes. In this paper we study a natural generalization of the random walk to a process in…