Related papers: Deterministic Approximation of Random Walks in Sma…
We establish scaling limits for the random walk whose state space is the range of a simple random walk on the four-dimensional integer lattice. These concern the asymptotic behaviour of the graph distance from the origin and the spatial…
We establish a central limit theorem, a local limit theorem, and a law of large numbers for a natural random walk on a symmetric space $M$ of non-compact type and rank one. This class of spaces, which includes the complex and quaternionic…
Analyzing social graphs with limited data access is challenging for third-party researchers. To address this challenge, a number of algorithms that estimate structural properties via a random walk have been developed. However, most existing…
For a directed graph $G$ with $n$ vertices and a start vertex $u_{\sf start}$, we wish to (approximately) sample an $L$-step random walk over $G$ starting from $u_{\sf start}$ with minimum space using an algorithm that only makes few passes…
We develop a new approach to random walks on de Bruijn graphs over the alphabet $A$ through right congruences on $A^k$, defined using the natural right action of $A^+$. A major role is played by special right congruences, which correspond…
A simple random walk on a graph is a sequence of movements from one vertex to another where at each step an edge is chosen uniformly at random from the set of edges incident on the current vertex, and then transitioned to next vertex.…
A quantum particle evolving by Schr\"odinger's equation contains, from the kinetic energy of the particle, a term in its Hamiltonian proportional to Laplace's operator. In discrete space, this is replaced by the discrete or graph Laplacian,…
Convolutional layers within graph neural networks operate by aggregating information about local neighbourhood structures; one common way to encode such substructures is through random walks. The distribution of these random walks evolves…
We define natural probability measures on cycle-rooted spanning forests (CRSFs) on graphs embedded on a surface with a Riemannian metric. These measures arise from the Laplacian determinant and depend on the choice of a unitary connection…
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…
We study discounted random walks in directed graphs. In each step, the walk either terminates with a constant probability $\alpha$, or proceeds to a random out-neighbor. Our goal is to estimate the probability $\pi(s, t)$ that a discounted…
We prove a quantitative Russo-Seymour-Welsh (RSW) type result for random walks on two natural examples of random planar graphs: the supercritical percolation cluster in the square lattice and the Poisson Voronoi triangulation in the plane.…
We present an efficient general method for realizing a quantum walk operator corresponding to an arbitrary sparse classical random walk. Our approach is based on Grover and Rudolph's method for preparing coherent versions of efficiently…
In this paper, we study Grover's search algorithm focusing on continuous-time quantum walk on graphs. We propose an alternative optimization approach to Grover's algorithm on graphs that can be summarized as follows: instead of finding…
We study the problem of approximately simulating a $t$-step random walk on a graph where the input edges come from a single-pass stream. The straightforward algorithm using reservoir sampling needs $O(nt)$ words of memory. We show that this…
We revisit an old minor topic in algorithms, the deterministic walk on a finite graph which always moves toward the nearest unvisited vertex until every vertex is visited. There is an elementary connection between this cover time and…
We introduce a stochastic global optimization method based on random walks on Grassmannian manifolds. To minimize a continuous objective $\ell:\mathbb{R}^d\rightarrow\mathbb{R}$, the method repeatedly samples random $k$-dimensional linear…
We give a deterministic algorithm for computing a global minimum vertex cut in a vertex-weighted graph $n$ vertices and $m$ edges in $\widehat O(mn)$ time. This breaks the long-standing $\widehat \Omega(n^{4})$-time barrier in dense graphs,…
We present a general method of designing fast approximation algorithms for cut-based minimization problems in undirected graphs. In particular, we develop a technique that given any such problem that can be approximated quickly on trees,…
We give new, improved bounds for approximating the sparsest cut value or in other words the conductance $\phi$ of a graph in the CONGEST model. As our main result, we present an algorithm running in $O(\log^2 n/\phi)$ rounds in which every…