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Related papers: Cover times and generic chaining

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We consider random walk on the structure given by a random hypergraph in the regime where there is a unique giant component. We give the asymptotics for hitting times, cover times, and commute times and show that the results obtained for…

Probability · Mathematics 2019-03-05 Amine Helali , Matthias Löwe

We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a…

Mathematical Physics · Physics 2009-10-20 Nikola Zlatanov , Ljupco Kocarev

We investigate the hitting times of random walks on graphs, where a hitting time is defined as the number of steps required for a random walker to move from one node to another. While much of the existing literature focuses on calculating…

Probability · Mathematics 2025-11-10 Anuraag Kumar

Using the results of Ding, Lee, Peres [3], we develop formulas to compute the hitting times and cover times for random walks on groups. We developed an explicit formula for hitting times in terms of the irreducible representations of the…

Probability · Mathematics 2023-02-07 Christopher Zhang

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.…

Probability · Mathematics 2012-02-28 Mohammed Abdullah

We analyze the covertime of a biased random walk on the random graph $G_{n,p}$. The walk is biased towards visiting vertices of low degree and this makes the covertime less than in the unbiased case

Combinatorics · Mathematics 2017-08-17 Colin Cooper , Alan Frieze , Samantha Petti

We pose a new and intriguing question motivated by distributed computing regarding random walks on graphs: How long does it take for several independent random walks, starting from the same vertex, to cover an entire graph? We study the…

Probability · Mathematics 2007-11-20 Noga Alon , Chen Avin , Michal Koucky , Gady Kozma , Zvi Lotker , Mark R. Tuttle

We introduce a cover time problem for random walks on dynamic graphs in which the graph expands in time and the walker moves at random times. Time to cover all nodes and number of returns to original states are analyzed in resulting model.

Probability · Mathematics 2023-03-02 Yunus Emre Demirci , Ümit Işlak , Mehmet Akif Yıldız

In this paper, following the paper ``On the average hitting times of the squares of cycles,'' we provide an explicit formula for the average hitting times of a simple random walk on a directed graph with $N$ vertices, where the graph…

Combinatorics · Mathematics 2026-01-27 Shunya Tamura

In this paper we show that on bounded degree graphs and general trees, the cover time of the simple random walk is asymptotically equal to the product of the number of edges and the square of the expected supremum of the Gaussian free field…

Probability · Mathematics 2014-02-26 Jian Ding

The cover time is defined as the time needed for a random walker to visit every site of a confined domain. Here, we focus on persistent random walks, which provide a minimal model of random walks with short range memory. We derive the exact…

Statistical Mechanics · Physics 2015-06-19 Marie Chupeau , Olivier Bénichou , Raphaël Voituriez

We introduce a new technique for bounding the cover time of random walks by relating it to the runtime of randomized broadcast. In particular, we strongly confirm for dense graphs the intuition of Chandra et al. \cite{CRRST97} that "the…

Data Structures and Algorithms · Computer Science 2009-02-11 Robert Elsässer , Thomas Sauerwald

We prove an explicit formula of hitting times in terms of enumerations of spanning trees for random walks on general connected graphs. We apply the formula to improve Lawler's bound of hitting times for general graphs, prove a sharp bound…

Combinatorics · Mathematics 2014-11-18 Hao Xu , Shing-Tung Yau

We present an analytical method for computing the mean cover time of a random walk process on arbitrary, complex networks. The cover time is defined as the time a random walker requires to visit every node in the network at least once. This…

Statistical Mechanics · Physics 2018-08-02 Benjamin F. Maier , Dirk Brockmann

We exhibit a close connection between hitting times of the simple random walk on a graph, the Wiener index, and related graph invariants. In the case of trees we obtain a simple identity relating hitting times to the Wiener index. It is…

Combinatorics · Mathematics 2015-12-15 Agelos Georgakopoulos , Stephan Wagner

Many known networks have structure of affiliation networks, where each of $n$ network's nodes (actors) selects an attribute set from a given collection of $m$ attributes and two nodes (actors) establish adjacency relation whenever they…

Combinatorics · Mathematics 2020-08-28 Mindaugas Bloznelis , Jerzy Jaworski , Katarzyna Rybarczyk

In recent years, protocols that are based on the properties of random walks on graphs have found many applications in communication and information networks, such as wireless networks, peer-to-peer networks and the Web. For wireless…

Networking and Internet Architecture · Computer Science 2009-07-13 Chen Avin , Yuval Lando , Zvi Lotker

A survey is presented of known results concerning simple random walk on the class of distance-regular graphs. One of the highlights is that electric resistance and hitting times between points can be explicitly calculated and given strong…

Probability · Mathematics 2013-01-29 Greg Markowsky

Random walk based distributed algorithms make use of a token that circulates in the system according to a random walk scheme to achieve their goal. To study their efficiency and compare it to one of the deterministic solutions, one is led…

Distributed, Parallel, and Cluster Computing · Computer Science 2008-07-24 Alain Bui , Devan Sohier

We study a random walk that prefers tou se unvisited edges in the context of random cubic graphs. We establish asymptotically correct estimates for the vertex and edge cover times, these being $\approx n\log n$ and $\approx \frac32n\log n$…

Combinatorics · Mathematics 2018-01-04 Colin Cooper , Alan Frieze , Tony Johansson
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