arXiv subjects
Publications and source records attributed to Amine Helali.
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 random walk on random graphs are universal.
The rate of convergence of the Gibbs sampler for the generalized one-dimensional Ising model is determined by the second largest eigenvalue of its transition matrix in absolute value denoted by $β^*$. In this paper we generalize a result from Shiu and Chen $(2015)$ for the one-dimensional Ising model with two states which gives a bound for $β^*$ . The method is based on Diaconis and Stroock bound for reversible Markov processes. The new bound presented in this paper improves Ingrassia's $(1994)$ result.
We study the geometric bound introduced by Diaconis and Stroock $(1991)$ of the Gibbs sampler for the two-dimensional Ising model with free boundary condition. The obtained result generalizes the method proposed by Shiu and Chen $(2015)$ from dimension one to dimension two. Furthermore we observe that the new bound improves the result given by Ingrassia $(1994)$.