Modified logarithmic Sobolev inequalities in null curvature
| dc.creator | Gentil, Ivan | |
| dc.creator | Guillin, Arnaud | |
| dc.creator | Miclo, Laurent | |
| dc.date | 2005-03-25 | |
| dc.date.accessioned | 2026-07-07T05:18:27Z | |
| dc.date.available | 2026-07-07T05:18:27Z | |
| dc.description | We present a logarithmic Sobolev inequality adapted to a log-concave measure. Assume that $Φ$ is a symmetric convex function on $\dR$ satisfying $(1+\e)Φ(x)\leq {x}Φ'(x)\leq(2-\e)Φ(x)$ for $x\geq0$ large enough and with $\e\in]0,1/2]$. We prove that the probability measure on $\dR$ $μ_Φ(dx)=e^{-Φ(x)}/Z_Φdx$ satisfies a modified and adapted logarithmic Sobolev inequality : there exist three constant $A,B,D>0$ such that for all smooth $f>0$, \begin{equation*} \ent{μ_Φ}{f^2}\leq A\int H_Φ\PAR{{\frac{f'}{f}}}f^2dμ_Φ, \text{with} H_Φ(x)= {\begin{array}{rl} Φ^*\PAR{Bx} &\text{if }\ABS{x}\geq D, x^2 &\text{if}\ABS{x}\leq D. \end{array} . \end{equation*} | |
| dc.identifier | https://arxiv.org/abs/math/0503585 | |
| dc.identifier | http://arxiv.org/abs/math/0503585 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74666 | |
| dc.subject | Probability | |
| dc.subject | Functional Analysis | |
| dc.title | Modified logarithmic Sobolev inequalities in null curvature | |
| dc.type | text |