Communications in Mathematical Sciences
Volume 12 (2014)
A few ways to destroy entropic chaoticity on Kac’s Sphere
Pages: 41 – 60
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