Communications in Mathematical Sciences

Volume 12 (2014)

Number 1

A few ways to destroy entropic chaoticity on Kac’s Sphere

Pages: 41 – 60



Amit Einav (Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, United Kingdom)


In this work we discuss a few ways to create chaotic families that are not entropically chaotic on Kac’s Sphere. We present two types of examples: limiting convex combinations of an entropically chaotic family with a particularly ‘bad’ non-entropic family, and two explicitly computable families that vary rapidly with $N$, causing loss of support on the sphere or high entropic tails.


Kac’s model, entropy, entropic chaoticity

2010 Mathematics Subject Classification

39B62, 60Fxx, 70Fxx

Published 20 August 2013