Convergence to Equilibrium of the Solution of Kac's Kinetic Equation. A Probabilistic View
Eugenio Regazzini (2009)
Bollettino dell'Unione Matematica Italiana
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Let be the probability density function representing the solution of Kac's Boltzmann-like equation at time , with initial data , and let be the Gaussian density with zero mean and variance , being the value of the second moment of . Henry McKean Jr. put forward the conjecture that the total variation distance between and goes to zero, as , with an exponential rate equal to . This lecture aims at explaining the main efforts made to a view to validating this conjecture,...