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Pré-Publication, Document De Travail Année : 2005

Self-Intersection Times for Random Walk, and Random Walk in Random Scenery

Résumé

We consider Random Walk in Random Scenery , denoted $X_n$, where the random walk is symmetric on $Z^d$, with $d>4$, and the random field is made up of i.i.d random variables with a stretched exponential tail decay, with exponent $\alpha$ with $1<\alpha$. We present asymptotics for the probability, over both randomness, that $\{X_n>n^{\beta}\}$ for $1/2<\beta<1$. To obtain such asymptotics, we establish large deviations estimates for the the self-intersection local times process.
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Dates et versions

hal-00009063 , version 1 (27-09-2005)

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  • HAL Id : hal-00009063 , version 1

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Amine Asselah, Fabienne Castell. Self-Intersection Times for Random Walk, and Random Walk in Random Scenery. 2005. ⟨hal-00009063⟩
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