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We prove Obata’s rigidity theorem for metric measure spaces that satisfy a Riemannian curvaturedimension condition. Additionally,we show that a lower bound K for the generalizedHessian of a sufficiently regular function u holds if and only if u is K-convex. A corollary is also a rigidity result for higher order eigenvalues.

Oblique derivative problems and invariant measures

I. Capuzzo Dolcetta, M. G. Garroni (1986)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Observations de M. Rouché en réponse à une Note de M. Delannoy

E. Rouché (1888)

Bulletin de la Société Mathématique de France

Occupation laws for some time-nonhomogeneous Markov chains.

Dietz, Zach, Sethuraman, Sunder (2007)

Electronic Journal of Probability [electronic only]

Occupation time sets of supports of continuous additive functionals

Cristina Gzyl, Henryk Gzyl (1979)

Annales de l'I.H.P. Probabilités et statistiques

Occupation times of branching systems with initial inhomogeneous Poisson states and related superprocesses.

Bojdecki, Tomasz, Gorostiza, Luis G., Talarczyk, Anna (2009)

Electronic Journal of Probability [electronic only]

Occupation times of compact sets by planar brownian motion

Terence Chan (1994)

Annales de l'I.H.P. Probabilités et statistiques

Occupation times of Lévy processes as quadratic variations

Nathalie Eisenbaum (2001)

Séminaire de probabilités de Strasbourg

Occurence times of rare events for mixing dynamical systems

A. Galves, B. Schmitt (1990)

Annales de l'I.H.P. Physique théorique

Occurrence of rare events in ergodic interacting spin systems

Amine Asselah, Paolo Dai Pra (1997)

Annales de l'I.H.P. Probabilités et statistiques

Odd cutsets and the hard-core model on $ℤ^{d}$

Ron Peled, Wojciech Samotij (2014)

Annales de l'I.H.P. Probabilités et statistiques

We consider the hard-core lattice gas model on $ℤ^{d}$ and investigate its phase structure in high dimensions. We prove that when the intensity parameter exceeds $C d^{- 1 / 3} {(log d)}^{2}$ , the model exhibits multiple hard-core measures, thus improving the previous bound of $C d^{- 1 / 4} {(log d)}^{3 / 4}$ given by Galvin and Kahn. At the heart of our approach lies the study of a certain class of edge cutsets in $ℤ^{d}$ , the so-called odd cutsets, that appear naturally as the boundary between different phases in the hard-core model. We provide a refined combinatorial...

On a Bernoulli Property of some Piecewise C2-Diffeomorphisms in ...d.

Piotr Bugiel (1993)

Monatshefte für Mathematik

On a Berry-Esseen type bound for the maximum likelihood estimator of a parameter for some stochastic partial differential equations.

Mishra, M.N., Prakasa Rao, B.L.S. (2004)

Journal of Applied Mathematics and Stochastic Analysis

On a bound on algebraic connectivity: the case of equality

Stephen J. Kirkland, Neumann, Michael, Bryan L. Shader (1998)

Czechoslovak Mathematical Journal

In a recent paper the authors proposed a lower bound on $1 - λ_{i}$ , where $λ_{i}$ , $λ_{i} \neq 1$ , is an eigenvalue of a transition matrix $T$ of an ergodic Markov chain. The bound, which involved the group inverse of $I - T$ , was derived from a more general bound, due to Bauer, Deutsch, and Stoer, on the eigenvalues of a stochastic matrix other than its constant row sum. Here we adapt the bound to give a lower bound on the algebraic connectivity of an undirected graph, but principally consider the case of equality in the bound when...

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