6 papers
Aldous' spectral gap phenomena in stochastic exchange models
Pietro Caputo, Matteo Quattropani, Federico Sau
We consider a broad class of exchange dynamics with arbitrary weighted graph or hypergraph update structures, which includes the Kipnis--Marchioro--Presutti (KMP) model and the ene…
-cutoff for the averaging process on random regular graphs
Pietro Caputo, Matteo Quattropani, Federico Sau
We study the mixing time of the averaging process on a large random -regular graph, , and prove an -cutoff with an explicit cutoff time. Somewhat surprisingly, we u…
Kac's Program and Relative Entropy Decay for Nonlinear Spin-Exchange Dynamics
Pietro Caputo, Mario Morellini
We introduce and analyze a nonlinear exchange dynamics for Ising spin systems with arbitrary interactions. The evolution is governed by a quadratic Boltzmann-type equation that con…
A universal cutoff phenomenon for mean-field exchange models
Pietro Caputo, Matteo Quattropani, Federico Sau
We study a broad class of high-dimensional mean-field exchange models, encompassing both noisy and singular dynamics, along with their dual processes. This includes a generalized v…
Repeated Block Averages: entropic time and mixing profiles
Pietro Caputo, Matteo Quattropani, Federico Sau
We consider randomized dynamics over the -simplex, where at each step a random set, or block, of coordinates is evenly averaged. When all blocks have size 2, this reduces to the…
Cutoff phenomenon in nonlinear recombinations
Pietro Caputo, Cyril Labbé, Hubert Lacoin
We investigate a quadratic dynamical system known as nonlinear recombinations. This system models the evolution of a probability measure over the Boolean cube, converging to the st…