31 citations · 134 across the 10 of their papers we have counts for
13 papers
Spectral Gaps for Reversible Markov Processes with Chaotic Invariant Measures: The Kac Process with Hard Sphere Collisions in Three Dimensions
Eric A. Carlen, Maria C. Carvalho, Michael P. Loss
We develop a method for producing estimates on the spectral gaps of reversible Markov jump processes with chaotic invariant measures, and we apply it to prove the Kac conjecture fo…
Chaos, Ergodicity and Equilibria in a Quantum Kac Model
Eric A. Carlen, Maria C. Carvalho, Michael P. Loss
We introduce quantum versions of the Kac Master Equation and the Kac Boltzmann Equation. We study the steady states of each of these equations, and prove a propagation of chaos the…
Entropy production inequalities for the Kac Walk
Eric A. Carlen, Maria C. Carvalho, Amit Einav
Mark Kac introduced what is now called 'the Kac Walk' with the aim of investigating the spatially homogeneous Boltzmann equation by probabilistic means. Much recent work, discussed…
A Boltzmann model for rod alignment and schooling fish
Eric a. Carlen, Maria C. Carvalho, Pierre Degond +1
We consider a Boltzmann model introduced by Bertin, Droz and Greegoire as a binary interaction model of the Vicsek alignment interaction. This model considers particles lying on th…
Spectral gap for the Kac model with hard sphere collisions
Eric A. Carlen, Maria C. Carvalho, Michael Loss
We prove the analog of the Kac conjecture for hard sphere collisions
Kinetic Theory and the Kac Master Equation
Eric Carlen, Maria C. Carvalho, Michael Loss
This article reviews recent work on the Kac master equation and its low dimensional counterpart, the Kac equation.