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The purpose of this article is to show that electrons and protons, interacting by Coulomb forces and governed by quantum statistical mechanics at suitable temperature and density, form a gas of Hydrogen atoms or molecules.

The best bounds in a theorem of Russell Lyons.

Marchal, Philippe (1998)

Electronic Communications in Probability [electronic only]

The center of mass of the ISE and the Wiener index of trees.

Janson, Svante, Chassaing, Philippe (2004)

Electronic Communications in Probability [electronic only]

The classical limit of reduced quantum stochastic evolutions

Robin Hudson, Martin Lindsay (1985)

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

The continuum reaction-diffusion limit of a stochastic cellular growth model

Stephan Luckhaus, Livio Triolo (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A competition-diffusion system, where populations of healthy and malignant cells compete and move on a neutral matrix, is analyzed. A coupled system of degenerate nonlinear parabolic equations is derived through a scaling procedure from the microscopic, Markovian dynamics. The healthy cells move much slower than the malignant ones, such that no diffusion for their density survives in the limit. The malignant cells may locally accumulate, while for the healthy ones an exclusion rule is considered....

The equivalence of the log-Sobolev inequality and a mixing condition for unbounded spin systems on the lattice

Nobuo Yoshida (2001)

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

The escape model on a homogeneous tree.

Kordzakhia, George (2005)

Electronic Communications in Probability [electronic only]

The foundations of probability with black swans.

Chichilnisky, Graciela (2010)

Journal of Probability and Statistics

The generalized weighted probability measure on the symmetric group and the asymptotic behavior of the cycles

Ashkan Nikeghbali, Dirk Zeindler (2013)

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

The goal of this paper is to analyse the asymptotic behaviour of the cycle process and the total number of cycles of weighted and generalized weighted random permutations which are relevant models in physics and which extend the Ewens measure. We combine tools from combinatorics and complex analysis (e.g. singularity analysis of generating functions) to prove that under some analytic conditions (on relevant generating functions) the cycle process converges to a vector of independent Poisson variables...