Global ETD Search
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Showing 1 to 6 of 6 for “"functional inequalities"”.
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Functional inequalities in quantum information theory
Functional inequalities constitute a very powerful toolkit in studying various problems arising in classical information theory, statistics and many-body systems. Extensions of these tools to the noncommutative setting have been introduced in the beginning of the 90's in order to study the …
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Functional inequalities and the curvature dimension inequality on totally geodesic foliations
… condition, we obtain (1) Sobolev-isoperimetric inequalities, global Poincar\'e inqualities, and a lower bound for Cheeger's isoperimetric constant, (2) Poincar\'e inequalities on balls and uniqueness of positive(or $L^p,p\geq 1$) solutions for the subelliptic heat equation, (3) A lower bound for …
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An optimization perspective on log-concave sampling and beyond
… gradient flows—through applications to functional inequalities, the entropic barrier, Wasserstein barycenters, variational inference, and diffusion models.
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Basic functional and geometric inequalities for the fractional order operators on homogenous Lie groups
In this PhD dissertation, we study functional and geometric inequalities on homo- geneous Lie groups. As for direct inequalities we obtain fractional Hardy, Sobolev, Hardy-Sobolev, Gagliardo-Nirenberg, Caffarelli-Kohn-Nirenberg, logarithmic inequal- ities, Hardy-Littlewood-Sobolev and Stein-Weiss …
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Convex Relaxations: Beyond Polynomials, Splitting Methods and Average Case Analysis
… formulate sum-of-squares relaxations of entropic functional inequalities including logarithmic Sobolev inequalities. We prove that our semidefinite programming hierarchies converge to the true logarithmic Sobolev constant of the finite Markov chain. This approach extends to other entropic …
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Keller-Segel-Type Models and Kinetic Equations for Interacting Particles: Long-Time Asymptotic Analysis
… of the equation and its associated free energy functional for which the overall convexity properties are not known. Special cases of this family of models have been investigated in previous works, and this part of the thesis represents a contribution towards a complete characterisation of the …