Year: 2015
Type: preprint
Abstract: Let $γ_n$ be the standard Gaussian measure on $\mathbb R^n$ and let $(Q_t)$ be the Ornstein--Ulhenbeck semigroup. Eldan and Lee recently established that for every non--negative function $f$ of integral $1$ and any time $t$ the following tail inequality holds true: \[ γ_n ( \{ Q_t f > r \} ) \leq C_t \, \frac{ (\log \log r)^4 }{r \sqrt{\log r}} , \quad \forall r>1 \] where $C_t$ is a constant depending on $t$ but not on the dimension. The purpose of the present paper is to simplify parts of their argument and to remove the $(\log \log r)^4$ factor.
Source: arXiv (Cornell University)
Author: Lehec, Joseph
Institution: Centre de Recherche en Mathématiques de la Décision
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2137232760