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pro vyhledávání: '"Serres, Jordan"'
Autor:
Serres, Jordan
We use a variational formulation to define a generalized notion of perimeter, from which we derive abstract isoperimetric Cheeger's inequalities via gradient estimates on solutions of Poisson equations. Our abstract framework unifies many existing re
Externí odkaz:
http://arxiv.org/abs/2411.05437
Autor:
Serres, Jordan
We adapt Stein's method to isoperimetric and geometric inequalities. The main challenge is the treatment of boundary terms. We address this by using an elliptic PDE with an oblique boundary condition. We apply our geometric formulation of Stein's met
Externí odkaz:
http://arxiv.org/abs/2410.20844
We generalize Gr\"unbaum's classical inequality in convex geometry to curved spaces with nonnegative Ricci curvature, precisely, to $\mathrm{RCD}(0,N)$-spaces with $N \in (1,\infty)$ as well as weighted Riemannian manifolds of $\mathrm{Ric}_N \ge 0$
Externí odkaz:
http://arxiv.org/abs/2408.15030
Barycenters (aka Fr\'echet means) were introduced in statistics in the 1940's and popularized in the fields of shape statistics and, later, in optimal transport and matrix analysis. They provide the most natural extension of linear averaging to non-E
Externí odkaz:
http://arxiv.org/abs/2303.01144
Autor:
Serres, Jordan
We control the behavior of the Poincar{\'e} constant along the Polchinski renormalization flow using a dynamic version of $\Gamma$-calculus. We also treat the case of higher order eigenvalues. Our method generalizes a method introduced by B. Klartag
Externí odkaz:
http://arxiv.org/abs/2208.08186
Autor:
Serres, Jordan
We study stability of the eigenvalues of the generator of a one dimensional reversible diffusion process satisfying some natural conditions. The proof is based on Stein's method. In particular, these results are applied to the Normal distribution (vi
Externí odkaz:
http://arxiv.org/abs/2205.15594
We study stability of the sharp spectral gap bounds for metric-measure spaces satisfying a curvature bound. Our main result, new even in the smooth setting, is a sharp quantitative estimate showing that if the spectral gap of an RCD$(N-1, N)$ space i
Externí odkaz:
http://arxiv.org/abs/2202.03769
Autor:
Serres, Jordan
We study stability of the sharp Poincar{\'e} constant of the invariant probability measure of a reversible diffusion process satisfying some natural conditions. The proof is based on the spectral interpretation of Poincar{\'e} inequalities and Stein'
Externí odkaz:
http://arxiv.org/abs/2105.12607
Autor:
Serres, Jordan
Publikováno v:
In Stochastic Processes and their Applications January 2023 155:459-484
Autor:
Serres, Jordan
Publikováno v:
Communications in Contemporary Mathematics; Sep2024, Vol. 26 Issue 7, p1-16, 16p