Binomial-Poisson entropic inequalities and the M/M/∞queue

DOI10.1051/ps:2006013zbMath1188.60047arXivmath/0510488OpenAlexW2593651454MaRDI QIDQ5429581

Djalil Chafaï

Publication date: 30 November 2007

Published in: ESAIM: Probability and Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0510488

zbMATH Keywords

entropyMarkov processesbirth and death processesqueuesfunctional inequalities

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Markov semigroups and applications to diffusion processes (47D07) Measures of information, entropy (94A17) Continuous-time Markov processes on discrete state spaces (60J27) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

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Cites Work

• Logarithmic Sobolev inequality for zero-range dynamics: independence of the number of particles
• Concentration inequalities and model selection. Ecole d'Eté de Probabilités de Saint-Flour XXXIII -- 2003.
• Loss networks
• On modified logarithmic Sobolev inequalities for Bernoulli and Poisson measures
• Variational formulas of Poincaré-type inequalities for birth-death processes.
• On logarithmic Sobolev inequalities for continuous time random walks on graphs
• A new modified logarithmic Sobolev inequality for Poisson point processes and several applications
• Moment inequalities for functions of independent random variables
• Entropy inequalities for unbounded spin systems
• Spectral gap estimates for interacting particle systems via a Bochner-type identity
• Logarithmic Sobolev inequality for zero-range dynamics
• Modified logarithmic Sobolev inequalities for some models of random walk
• On limit laws for service processes in multi-channel systems
• Logarithmic Sobolev inequalities for finite Markov chains
• Entropies, convexity, and functional inequalities: on \(\Phi\)-entropies and \(\Phi\)-Sobolev inequalities
• Entropy dissipation estimates in a zero-range dynamics
• Modified log-sobolev inequalities, mixing and hypercontractivity
• Blocking probabilities in large circuit-switched networks
• Markov Chains
• Functional inequalities for discrete gradients and application to the geometric distribution
• Preservation of log-concavity on summation
• Clark-Ocone formulas and Poincaré inequalities of the discrete cube
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