Zobrazeno 1 - 10
of 254
pro vyhledávání: '"Caputo, Pietro"'
We consider randomized dynamics over the $n$-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 repeated averages studied in [CDSZ22], a version of the averaging pro
Externí odkaz:
http://arxiv.org/abs/2407.16656
Autor:
Caputo, Pietro, Salez, Justin
We develop a new framework for establishing approximate factorization of entropy on arbitrary probability spaces, using a geometric notion known as non-negative sectional curvature. The resulting estimates are equivalent to entropy subadditivity and
Externí odkaz:
http://arxiv.org/abs/2407.13457
We discuss the relaxation time (inverse spectral gap) of the one dimensional $O(N)$ model, for all $N$ and with two types of boundary conditions. We see how its low temperature asymptotic behavior is affected by the topology. The combination of the s
Externí odkaz:
http://arxiv.org/abs/2407.12610
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 stationary state obtained as the product of the initial marginals. Our m
Externí odkaz:
http://arxiv.org/abs/2402.11396
We study Markov chains with non-negative sectional curvature on finite metric spaces. Neither reversibility, nor the restriction to a particular combinatorial distance are imposed. In this level of generality, we prove that a 1-step contraction in th
Externí odkaz:
http://arxiv.org/abs/2401.17148
Gibbsian line ensembles are families of Brownian lines arising in many natural contexts such as the level curves of three dimensional Ising interfaces, the solid-on-solid model, multi-layered polynuclear growth etc. An important example is a class of
Externí odkaz:
http://arxiv.org/abs/2310.06817
Autor:
Caputo, Pietro, Sinclair, Alistair
We introduce and analyze a natural class of nonlinear dynamics for spin systems such as the Ising model. This class of dynamics is based on the framework of mass action kinetics, which models the evolution of systems of entities under pairwise intera
Externí odkaz:
http://arxiv.org/abs/2305.18788
Autor:
Caputo, Pietro, Ganguly, Shirshendu
We consider non-colliding Brownian lines above a hard wall, which are subject to geometrically growing (given by a parameter $\lambda>1$) area tilts, which we call the $\lambda$-tilted line ensemble (LE). The model was introduced by Caputo, Ioffe, Wa
Externí odkaz:
http://arxiv.org/abs/2305.18280
We consider the averaging process on a graph, that is the evolution of a mass distribution undergoing repeated averages along the edges of the graph at the arrival times of independent Poisson processes. We establish cutoff phenomena for both the $L^
Externí odkaz:
http://arxiv.org/abs/2212.08870
Autor:
Caputo, Pietro, Parisi, Daniel
We study a nonlinear recombination model from population genetics as a combinatorial version of the Kac-Boltzmann equation from kinetic theory. Following Kac's approach, the nonlinear model is approximated by a mean field linear evolution with a larg
Externí odkaz:
http://arxiv.org/abs/2207.04775