# Ornstein-Uhlenbeck pinball and the Poincaré inequality in a punctured domain.

@inproceedings{Boissard2018OrnsteinUhlenbeckPA, title={Ornstein-Uhlenbeck pinball and the Poincar{\'e} inequality in a punctured domain.}, author={Emmanuel Boissard and P. Cattiaux and A. Guillin and L. Miclo}, year={2018} }

In this paper we study the Poincare constant for the Gaussian measure restricted to \(D={\mathbb R}^d - \mathbb {B}\) where \(\mathbb {B}\) is the disjoint union of bounded open sets. We will mainly look at the case where the obstacles are Euclidean balls B(xi, ri) with radii ri, or hypercubes with vertices of length 2ri, and d ≥ 2. This will explain the asymptotic behavior of a d-dimensional Ornstein-Uhlenbeck process in the presence of obstacles with elastic normal reflections (the Ornstein… CONTINUE READING

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