On the distribution of random walk local time
A. N. Borodin (1987)
Annales de l'I.H.P. Probabilités et statistiques
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A. N. Borodin (1987)
Annales de l'I.H.P. Probabilités et statistiques
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Françoise Pène (2009)
Annales de l'I.H.P. Probabilités et statistiques
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We consider the periodic planar Lorentz process with convex obstacles (and with finite horizon). In this model, a point particle moves freely with elastic reflection at the fixed convex obstacles. The random scenery is given by a sequence of independent, identically distributed, centered random variables with finite and non-null variance. To each obstacle, we associate one of these random variables. We suppose that each time the particle hits an obstacle, it wins the amount given by...
Amine Asselah (2011)
Annales de l'I.H.P. Probabilités et statistiques
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We study the upper tails for the energy of a randomly charged symmetric and transient random walk. We assume that only charges on the same site interact pairwise. We consider estimates, that is when we average over both randomness, in dimension three or more. We obtain a large deviation principle, and an explicit rate function for a large class of charge distributions.
Bogdan Iftimie, Étienne Pardoux, Andrey Piatnitski (2008)
Annales de l'I.H.P. Probabilités et statistiques
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This paper deals with the homogenization problem for a one-dimensional parabolic PDE with random stationary mixing coefficients in the presence of a large zero order term. We show that under a proper choice of the scaling factor for the said zero order terms, the family of solutions of the studied problem converges in law, and describe the limit process. It should be noted that the limit dynamics remain random.
A. Plucińska (1962)
Colloquium Mathematicae
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Kerbashev, Tzvetozar (1999)
Serdica Mathematical Journal
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The maximum M of a critical Bienaymé-Galton-Watson process conditioned on the total progeny N is studied. Imbedding of the process in a random walk is used. A limit theorem for the distribution of M as N → ∞ is proved. The result is trasferred to the non-critical processes. A corollary for the maximal strata of a random rooted labeled tree is obtained.