Related papers: Colored loop-erased random walk on the complete gr…
We base ourselves on the construction of the two-dimensional random interlacements [12] to define the one-dimensional version of the process. For this constructions we consider simple random walks conditioned on never hitting the origin,…
Random walks find extensive application across various complex network domains, including embedding generation and link prediction. Despite the widespread utilization of random walks, the precise impact of distinct biases on embedding…
We consider uniform random permutations drawn from a family enumerated through generating trees. We develop a new general technique to establish a central limit theorem for the number of consecutive occurrences of a fixed pattern in such…
We present analytical results for the distribution of first return (FR) times of random walks (RWs) on random regular graphs (RRGs) consisting of $N$ nodes of degree $c \ge 3$. Starting from a random initial node $i$ at time $t=0$, at each…
We study the excited random walk, in which a walk that is at a site that contains cookies eats one cookie and then hops to the right with probability p and to the left with probability q=1-p. If the walk hops onto an empty site, there is no…
We study discrete-time random walks on arbitrary networks with first-passage resetting processes. To the end, a set of nodes are chosen as observable nodes, and the walker is reset instantaneously to a given resetting node whenever it hits…
We focus on the problem of performing random walks efficiently in a distributed network. Given bandwidth constraints, the goal is to minimize the number of rounds required to obtain a random walk sample. We first present a fast sublinear…
Graph embedding has recently gained momentum in the research community, in particular after the introduction of random walk and neural network based approaches. However, most of the embedding approaches focus on representing the local…
A constructive proof is given to the fact that any ergodic Markov chain can be realized as a random walk subject to a synchronizing road coloring. Redundancy (ratio of extra entropy) in such a realization is also studied.
An edge-locating coloring of a simple connected graph $G$ is a partition of its edge set into matchings such that the vertices of $G$ are distinguished by the distance to the matchings. The minimum number of the matchings of $G$ that admits…
This paper considers non-backtracking random walks on random graphs generated according to the configuration model. The quantity of interest is the scaling of the mixing time of the random walk as the number of vertices of the random graph…
We provide a decomposition of the trace of the Brownian motion into a simple path and an independent Brownian soup of loops that intersect the simple path. More precisely, we prove that any subsequential scaling limit of the loop erased…
We prove strong theorems for the local time at infinity of a nearest neighbor transient random walk. First, laws of the iterated logarithm are given for the large values of the local time. Then we investigate the length of intervals over…
In this article, we study linearly edge-reinforced random walk on general multi-level ladders for large initial edge weights. For infinite ladders, we show that the process can be represented as a random walk in a random environment, given…
We study the time evolution of continuous-time quantum walks on randomly changing graphs. At certain moments edges of the graph appear or disappear with a given probability. We focus on the case when the time interval between subsequent…
We consider biased random walk on regular tree and we obtain the spectral radius, first return probability and $n$-step transition probability.
We study an intermittent random walk on a random network of scale-free degree distribution. The walk is a combination of simple random walks of duration $t_w$ and random long-range jumps. While the time the walker needs to cover all the…
We consider a model of loop-erased random walks on the finite pre-Sierpinski gasket which permits rigorous analysis. We prove the existence of the scaling limit and show that the path of the limiting process is almost surely self-avoiding,…
A spanning tree of an edge-colored graph is rainbow provided that each of its edges receives a distinct color. In this paper we consider the natural extremal problem of maximizing and minimizing the number of rainbow spanning trees in a…
Circular coloring is a constraints satisfaction problem where colors are assigned to nodes in a graph in such a way that every pair of connected nodes has two consecutive colors (the first color being consecutive to the last). We study…