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10 papers · 2 filters
Mixing time of exponential random graphs
Shankar Bhamidi, Guy Bresler, Allan Sly
Exponential random graphs are used extensively in the sociology literature. This model seeks to incorporate in random graphs the notion of reciprocity, that is, the larger than exp…
Coagulation, diffusion and the continuous Smoluchowski equation
Mohammad Reza Yaghouti, Fraydoun Rezakhanlou, Alan Hammond
The Smoluchowski equation is a system of partial differential equations modelling the diffusion and binary coagulation of a large collection of tiny particles. The mass parameter m…
An observation about submatrices
Sourav Chatterjee, Michel Ledoux
Let M be an arbitrary Hermitian matrix of order n, and k be a positive integer less than or equal to n. We show that if k is large, the distribution of eigenvalues on the real line…
The mixing time evolution of Glauber dynamics for the mean-field Ising model
Jian Ding, Eyal Lubetzky, Yuval Peres
We consider Glauber dynamics for the Ising model on the complete graph on vertices, known as the Curie-Weiss model. It is well-known that the mixing-time in the high temperatur…
Exact conditions for no ruin for the generalised Ornstein-Uhlenbeck process
Damien Bankovsky, Allan Sly
For a bivariate Lévy process the generalised Ornstein-Uhlenbeck (GOU) process is defined as V_t:=e^{ξ_t}(z+\int_0^t e^{-ξ_{s-}}dη_s), t\ge0, where $z\in\mathb…
The Phase Diagram of the Quantum Curie-Weiss Model
Lincoln Chayes, Nicholas Crawford, Dmitry Ioffe +1
This paper studies a generalization of the Curie-Weiss model (the Ising model on a complete graph) to quantum mechanics. Using a natural probabilistic representation of this model,…