The maximum entropy principle and volumetric properties of Orlicz balls

We study the precise asymptotic volume of balls in Orlicz spaces and show that intersection two undergoes a phase transition when dimension ambient space tends to infinity. This generalizes result Schechtman Schmuckenschläger (1991) [32] for ℓpd-balls. As another application, we determine ratio 2-concave ℓMd. Our method rests on ideas from statistical mechanics large deviations theory, more precisely maximum entropy or Gibbs principle non-interacting particles, presents natural approach fresh perspective such geometric volumetric questions. In particular, our explains how p-generalized Gaussian distribution occurs problems related geometry ℓpd-balls, which are function is M(t)=|t|p.