5 papers · 1 filter
-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…
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…
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…