23 citations · 72 across the 17 of their papers we have counts for
8 papers · 1 filter
Improvement of Wu's logarithmic Sobolev inequality via the Poisson-Föllmer process
Shrey Aryan, Pablo López-Rivera, Yair Shenfeld
We give an alternative proof to Wu's logarithmic Sobolev inequality for the Poisson measure on the nonnegative integers using a stochastic variational formula for entropy. We show…
The Poisson transport map
Pablo López-Rivera, Yair Shenfeld
We construct a transport map from Poisson point processes onto ultra-log-concave measures over the natural numbers, and show that this map is a contraction. Our approach overcomes…
Transportation onto log-Lipschitz perturbations
Max Fathi, Dan Mikulincer, Yair Shenfeld
We establish sufficient conditions for the existence of globally Lipschitz transport maps between probability measures and their log-Lipschitz perturbations, with dimension-free bo…
Intrinsic dimensional functional inequalities on model spaces
Alexandros Eskenazis, Yair Shenfeld
We initiate a systematic study of intrinsic dimensional versions of classical functional inequalities which capture refined properties of the underlying objects. We focus on model…
On the Lipschitz properties of transportation along heat flows
Dan Mikulincer, Yair Shenfeld
We prove new Lipschitz properties for transport maps along heat flows, constructed by Kim and Milman. For (semi)-log-concave measures and Gaussian mixtures, our bounds have several…
The Brownian transport map
Dan Mikulincer, Yair Shenfeld
Contraction properties of transport maps between probability measures play an important role in the theory of functional inequalities. The actual construction of such maps, however…
Stability of the logarithmic Sobolev inequality via the Föllmer Process
Ronen Eldan, Joseph Lehec, Yair Shenfeld
We study the stability and instability of the Gaussian logarithmic Sobolev inequality, in terms of covariance, Wasserstein distance and Fisher information, addressing several open…
The equality cases of the Ehrhard-Borell inequality
Yair Shenfeld, Ramon van Handel
The Ehrhard-Borell inequality is a far-reaching refinement of the classical Brunn-Minkowski inequality that captures the sharp convexity and isoperimetric properties of Gaussian me…