Hitting times, commute times, and cover times for random walks on random hypergraphs

@article{Helali2019HittingTC,
  title={Hitting times, commute times, and cover times for random walks on random hypergraphs},
  author={Amine Helali and Matthias Lowe},
  journal={Statistics \& Probability Letters},
  year={2019}
}
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8 Citations
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8 Citations

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References

SHOWING 1-10 OF 16 REFERENCES

The cover times of random walks on random uniform hypergraphs

The Cover Times of Random Walks on Hypergraphs

An expression for C(H) is given which is tractable for many classes of hypergraphs, and C (H) and I(H ) are calculated exactly for random r-regular, s-uniform hyper graphs.

Random Walks on Graphs: a Survey

Dedicated to the marvelous random walk of Paul Erd} os through universities, c ontinents, and mathematics Various aspects of the theory of random walks on graphs are surveyed. In particular,…

First-passage properties of the Erdos Renyi random graph

An effective medium approximation is developed that predicts that the mean first-passage time between pairs of nodes, as well as all moments of this first- passage time, are insensitive to the fraction p of occupied links.

Asymptotic normality of the size of the giant component in a random hypergraph

It is shown that the same method applies to the analogous model of random k ‐uniform hypergraphs, establishing asymptotic normality throughout the (sparse) supercritical regime.

Random Walks on Infinite Graphs and Groups

Part I. The Type Problem: 1. Basic facts 2. Recurrence and transience of infinite networks 3. Applications to random walks 4. Isoperimetric inequalities 5. Transient subtrees, and the classification…

Spectral statistics of Erdős–Rényi graphs I: Local semicircle law

We consider the ensemble of adjacency matrices of Erdős–Renyi random graphs, that is, graphs on N vertices where every edge is chosen independently and with probability p≡p(N). We rescale the matrix…

A phase transition for the limiting spectral density of random matrices

We analyze the spectral distribution of symmetric random matrices with correlated entries. While we assume that the diagonals of these random matrices are stochastically independent, the elements of…

Markov Chains and Mixing Times

This book is an introduction to the modern approach to the theory of Markov chains. The main goal of this approach is to determine the rate of convergence of a Markov chain to the stationary…

On hitting times for simple random walk on dense Erd\"os-R\'enyi random graphs