In this paper, we consider the harmonic measure on the unit sphere Sn−1 on Rn (n≥2) and offer a two-sided estimate of precise order on the Sobolev constant with exponent p∈(1,2). As special cases for p=1 and p tending to 2, our estimates recover those in Barthe et al. (2104) for n≥3...

For an exchangeable sequence of random variables taking values in a Polish space, we obtain a necessary and sufficient condition for the large deviation principles with respect to the [tau]-topology of the occupation measure and of the process-level empirical measures.

By using the existing sharp estimates of the density function for rotationally invariant symmetric [alpha]-stable Lévy processes and rotationally invariant symmetric truncated [alpha]-stable Lévy processes, we obtain that the Harnack inequalities hold for rotationally invariant symmetric...

We present sharp asymptotic limit properties of the maximum of the occupation measure around intervals for a transient Brownian sheet. The corresponding multifractal analysis via packing dimension for occupation measures is also established.