Stochastic Processes and their Applications

On the maximal dimension of random simplicial complexes

The dimension of random simplicial complexes (defined as the maximal dimension among all faces) is a natural extreme value associated with the complex, and is closely related to other functionals defined by a maximum, such as the clique number of geometric graphs or scan statistics. We extend existing results in the...

Random Recursive Simplicial Complexes

We investigate random recursive simplicial complexes growing by adding, at each step, a vertex together with a simplex formed by joining the new vertex with a randomly chosen existing simplex. We also add all faces of the new simplex to ensure that the resulting object remains a simplicial complex. If the choice of an...

Markov chains arising in the study of random matrices over pro-finite rings

Recent work of the author investigates certain random processes, valued in abelian p-groups, that naturally arise in the study of Haar random matrices over $\mathbb{Z}_p$. It was found, somewhat surprisingly, that these processes are reversible Markov chains. In this short note, we give a simple alternative derivation...

European Journal of Combinatorics

A dynamic point of view on universality for random matrices over finite local rings

We consider the cokernel corners process for an i.i.d. matrix with entries in a finite local ring. When the distribution of the entries is uniform, this process is a Markov chain, and hence the ergodic theorem for Markov chains can be applied. This implies, in particular, that for uniformly distributed p-adic random ma...

Monotonicity and decompositions of random regular graphs

In this work we establish several monotonicity and decomposition results in the framework of random regular graphs. Among other results, we show that, for a wide range of parameters d1≤d2, there exists a coupling of G(n,d1) and G(n,d2) satisfying that G(n,d1)⊆G(n,d2) with high probability, confirming a conjecture of Ga...