Sur les in'egalit'es de Sobolev logarithmiques

By Cécile Ané, S. Blachère, Djalil CHAFAÏ, Pierre Fougères, Ivan Gentil, Florent Malrieu, Cyril Roberto, Grégory Scheffer. 2000

190 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/e6a910221bef2589164cb744ff0b07cff52ad2eb

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Citations in the corpus

Poincaré inequalities on intervals – application to sensitivity analysis (2016, unknown): “The equality case is well-known (see e.g. [3]).”
Strong asymptotic freeness for Wigner and Wishart matrices preprint (2005, unknown): “We refer the reader to [4] for a characterization of the measures on R which satisfy a Poincar´e inequality (see also [1]).”
Characterization of Talagrand's like transportation-cost inequalities on the real line (2006, background): “Let θp be defined by θp(x)= { x2 if |x| 1, 2 p |x|p + 1 − 2 p if |x| 1, ∀p ∈ [1,2].”
Functional Inequalities for Markov semigroups (2009, background): “We shall not give any detail of the proof here (the reader may consult [3] or [5], for example).”
Riemannian Ricci curvature lower bounds in metric measure spaces with -finite measure (2012, unknown): “[7].”
Ricci curvature for metric-measure spaces via optimal transport (2004, background): “All of these inequalities are associated with concentration of measure [4, 8, 9, 26, 27].”
Some geometric properties of the Bakry-Émery-Ricci tensor (2002, background): “We refer to [2] and [19] for information on these connections.”
Coercive Inequalities on Metric Measure Spaces (2009, result): “The proof is similar to that of Theorem 2.2”
Bernstein type's concentration inequalities for symmetric Markov processes (2010, methodology): “The first one, initiated by Ledoux, relies on functional inequalities, such as Poincaré or logarithmic Sobolev inequality (see for example [2] or [33]) and has attracted a lot of attention in the past decade: Wu [51] or Cattiaux-Guillin [15] used them in the continuous time context to get precise co”
Mass Transport and Variants of the Logarithmic Sobolev Inequality (2007, background): “[5, 7, 23, 41, 42, 48, 57].”
Curvature and transport inequalities for Markov chains in discrete spaces (2015, background): “ develop some more: Proposition 2.2. (Convexity) Let gbe a function deﬁned on X, then for all x∈ X, the function t→ Qetg(x) is convex. Proof. Fix x ∈ X, deﬁne G(t) := Qetg(x) Observe that for any λ ∈ [0,1], and p1,p2 ∈ P(X), setting p:= λp1 + (1 − λ)p2 ∈ P(X) and applying the CauchySchwarz inequalit”