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12 papers · 2 filters
A note on the tensor product of two random unitary matrices
Tomasz Tkocz
In this note we consider the point process of eigenvalues of the tensor product of two independent random unitary matrices of size m by m and n by n. When n becomes large, the proc…
Feynman-Kac particle integration with geometric interacting jumps
Pierre Del Moral, Pierre E. Jacob, Anthony Lee +2
This article is concerned with the design and analysis of discrete time Feynman-Kac particle integration models with geometric interacting jump processes. We analyze two general ty…
Random walks on Galton-Watson trees with infinite variance offspring distribution conditioned to survive
David A. Croydon, Takashi Kumagai
We establish a variety of properties of the discrete time simple random walk on a Galton-Watson tree conditioned to survive when the offspring distribution, say, is in the doma…
Self-similarity and spectral asymptotics for the continuum random tree
D. A. Croydon, B. M. Hambly
We use the random self-similarity of the continuum random tree to show that it is homeomorphic to a post-critically finite self-similar fractal equipped with a random self-similar…
Scaling limit for the random walk on the largest connected component of the critical random graph
David A. Croydon
A scaling limit for the simple random walk on the largest connected component of the Erdos-Renyi random graph in the critical window is deduced. The limiting diffusion is construct…
Heat kernel fluctuations for a resistance form with non-uniform volume growth
David A. Croydon
In this article, we consider the problem of estimating the heat kernel on measure-metric spaces equipped with a resistance form. Such spaces admit a corresponding resistance metric…