Displaying similar documents to “First hitting times of simple random walks on graphs with congestion points.”

Excited random walk.

Benjamini, Itai, Wilson, David B. (2003)

Electronic Communications in Probability [electronic only]

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Discrete random processes with memory: Models and applications

Tomáš Kouřim, Petr Volf (2020)

Applications of Mathematics

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The contribution focuses on Bernoulli-like random walks, where the past events significantly affect the walk's future development. The main concern of the paper is therefore the formulation of models describing the dependence of transition probabilities on the process history. Such an impact can be incorporated explicitly and transition probabilities modulated using a few parameters reflecting the current state of the walk as well as the information about the past path. The behavior...

Infinite paths and cliques in random graphs

Alessandro Berarducci, Pietro Majer, Matteo Novaga (2012)

Fundamenta Mathematicae

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We study the thresholds for the emergence of various properties in random subgraphs of (ℕ, <). In particular, we give sharp sufficient conditions for the existence of (finite or infinite) cliques and paths in a random subgraph. No specific assumption on the probability is made. The main tools are a topological version of Ramsey theory, exchangeability theory and elementary ergodic theory.

Giant vacant component left by a random walk in a random d-regular graph

Jiří Černý, Augusto Teixeira, David Windisch (2011)

Annales de l'I.H.P. Probabilités et statistiques

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We study the trajectory of a simple random walk on a -regular graph with ≥ 3 and locally tree-like structure as the number of vertices grows. Examples of such graphs include random -regular graphs and large girth expanders. For these graphs, we investigate percolative properties of the set of vertices not visited by the walk until time , where &gt; 0 is a fixed positive parameter. We show that this so-called set exhibits a phase transition in in the following sense: there exists...