Mirrored langevin dynamics
We consider the problem of sampling from constrained distributions, which has posed
significant challenges to both non-asymptotic analysis and algorithmic design. We propose …
significant challenges to both non-asymptotic analysis and algorithmic design. We propose …
Wasserstein mirror gradient flow as the limit of the Sinkhorn algorithm
We prove that the sequence of marginals obtained from the iterations of the Sinkhorn
algorithm or the iterative proportional fitting procedure (IPFP) on joint densities, converges to …
algorithm or the iterative proportional fitting procedure (IPFP) on joint densities, converges to …
Stein kernels and moment maps
M Fathi - The Annals of Probability, 2019 - JSTOR
We describe a construction of Stein kernels using moment maps, which are solutions to a
variant of the Monge–Ampère equation. As a consequence, we show how regularity bounds …
variant of the Monge–Ampère equation. As a consequence, we show how regularity bounds …
Quantitative stability of the entropy power inequality
TA Courtade, M Fathi… - IEEE Transactions on …, 2018 - ieeexplore.ieee.org
We establish quantitative stability results for the entropy power inequality (EPI). Specifically,
we show that if uniformly log-concave densities nearly saturate the EPI, then they must be …
we show that if uniformly log-concave densities nearly saturate the EPI, then they must be …
Riemannian metrics on convex sets with applications to Poincaré and log-Sobolev inequalities
AV Kolesnikov, E Milman - Calculus of Variations and Partial Differential …, 2016 - Springer
Given a probability measure μ μ supported on a convex subset Ω Ω of Euclidean space (R^
d, g_0)(R d, g 0), we are interested in obtaining Poincaré and log-Sobolev type inequalities …
d, g_0)(R d, g 0), we are interested in obtaining Poincaré and log-Sobolev type inequalities …
On weighted Blaschke--Santalo and strong Brascamp--Lieb inequalities
A Colesanti, A Kolesnikov, G Livshyts… - arXiv preprint arXiv …, 2024 - arxiv.org
arXiv:2409.11503v1 [math.FA] 17 Sep 2024 Page 1 arXiv:2409.11503v1 [math.FA] 17 Sep
2024 On weighted Blaschke–Santaló and strong Brascamp–Lieb inequalities Andrea …
2024 On weighted Blaschke–Santaló and strong Brascamp–Lieb inequalities Andrea …
Mass transportation functionals on the sphere with applications to the logarithmic Minkowski problem
AV Kolesnikov - arXiv preprint arXiv:1807.07002, 2018 - arxiv.org
We study the transportation problem on the unit sphere $ S^{n-1} $ for symmetric probability
measures and the cost function $ c (x, y)=\log\frac {1}{\langle x, y\rangle} $. We calculate the …
measures and the cost function $ c (x, y)=\log\frac {1}{\langle x, y\rangle} $. We calculate the …
Logarithmically-concave moment measures I
B Klartag - Geometric Aspects of Functional Analysis: Israel …, 2014 - Springer
We discuss a certain Riemannian metric, related to the toric Kähler-Einstein equation, that is
associated in a linearly-invariant manner with a given log-concave measure in R^ n. We use …
associated in a linearly-invariant manner with a given log-concave measure in R^ n. We use …
Free Stein Kernel and Moments maps
CP Diez - arXiv preprint arXiv:2410.02470, 2024 - arxiv.org
In this paper we propose a free analogue to Fathi's construction of Stein kernels using
moment maps (2019). This is possible for a class of measures called free moment …
moment maps (2019). This is possible for a class of measures called free moment …
[HTML][HTML] Convergence of metric measure spaces satisfying the CD condition for negative values of the dimension parameter
M Magnabosco, C Rigoni, G Sosa - Nonlinear Analysis, 2023 - Elsevier
We study the problem of whether the curvature-dimension condition with negative values of
the generalized dimension parameter is stable under a suitable notion of convergence. To …
the generalized dimension parameter is stable under a suitable notion of convergence. To …