Random walk in random environment with asymptotically zero perturbation

M.V. Menshikov; Andrew R. Wade

Displaying similar documents to “Random walk in random environment with asymptotically zero perturbation”

Perturbing transient random walk in a random environment with cookies of maximal strength

Elisabeth Bauernschubert (2013)

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

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We consider a left-transient random walk in a random environment on $ℤ$ that will be disturbed by cookies inducing a drift to the right of strength 1. The number of cookies per site is i.i.d. and independent of the environment. Criteria for recurrence and transience of the random walk are obtained. For this purpose we use subcritical branching processes in random environments with immigration and formulate criteria for recurrence and transience for these processes.

Slowdown estimates and central limit theorem for random walks in random environment

Alain-Sol Sznitman (2000)

Journal of the European Mathematical Society

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This work is concerned with asymptotic properties of multi-dimensional random walks in random environment. Under Kalikow’s condition, we show a central limit theorem for random walks in random environment on $ℤ^{d}$ , when $d > 2$ . We also derive tail estimates on the probability of slowdowns. These latter estimates are of special interest due to the natural interplay between slowdowns and the presence of traps in the medium. The tail behavior of the renewal time constructed in [25] plays an important...

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R. Kaufman (1970)

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On the existence and asymptotic behavior of the random solutions of the random integral equation with advancing argument

Henryk Gacki (1996)

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1. Introduction Random Integral Equations play a significant role in characterizing of many biological and engineering problems [4,5,6,7]. We present here new existence theorems for a class of integral equations with advancing argument. Our method is based on the notion of a measure of noncompactness in Banach spaces and the fixed point theorem of Darbo type. We shall deal with random integral equation with advancing argument $x (t, ω) = h (t, ω) + \int^{t + δ (t)} ₀ k (t, τ, ω) f (τ, x_{τ} (ω)) d τ$ , (t,ω) ∈ R⁺ × Ω, (1) where (i) (Ω,A,P) is a complete probability...

On coincidences in renewal streams

I. Kopocińska, B. Kopociński (1987)

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Strong disorder in semidirected random polymers

N. Zygouras (2013)

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

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We consider a random walk in a random potential, which models a situation of a random polymer and we study the annealed and quenched costs to perform long crossings from a point to a hyperplane. These costs are measured by the so called Lyapounov norms. We identify situations where the point-to-hyperplane annealed and quenched Lyapounov norms are different. We also prove that in these cases the polymer path exhibits localization.

Random dynamics and its applications.

Kifer, Yuri (1998)

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Some random coincidence and random fixed point theorems for hybrid contractions.

Mustafa, Ghulam, Nosh, Nusrat Anjum, Rashid, Abdur (2005)

Lobachevskii Journal of Mathematics

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On the probabilistic properties of the solution of random integral equations

Nguyen, Quy Hy, Nguyen, Ngoc Cuong (2015-12-08T12:59:38Z)

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On the distance random variable

G. Trybuś (1974)

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Excited against the tide: a random walk with competing drifts

Mark Holmes (2012)

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

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We study excited random walks in i.i.d. random cookie environments in high dimensions, where the $k$ th cookie at a site determines the transition probabilities (to the left and right) for the $k$ th departure from that site. We show that in high dimensions, when the expected right drift of the first cookie is sufficiently large, the velocity is strictly positive, regardless of the strengths and signs of subsequent cookies. Under additional conditions on the cookie environment, we show that...

Scaling of a random walk on a supercritical contact process

F. den Hollander, R. S. dos Santos (2014)

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

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We prove a strong law of large numbers for a one-dimensional random walk in a dynamic random environment given by a supercritical contact process in equilibrium. The proof uses a coupling argument based on the observation that the random walk eventually gets trapped inside the union of space–time cones contained in the infection clusters generated by single infections. In the case where the local drifts of the random walk are smaller than the speed at which infection clusters grow, the...

Optimal stopping of a random length sequence of maxima over a random barrier

Z. Porosiński (1988)

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On the exact distributional asymptotics for the supremum of a random walk with increments in a class of light-tailed distribution.

Zachary, Stan, Foss, S.G. (2006)

Sibirskij Matematicheskij Zhurnal

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Superdiffusivity for directed polymer in corelated random environment

Hubert Lacoin (2010)

Actes des rencontres du CIRM

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The directed polymer in random environment models the behavior of a polymer chain in a solution with impurities. It is a particular case of random walk in random environment. In $1 + 1$ dimensional environment is has been shown by Petermann that this random walk is superdiffusive. We show superdiffusivity properties are reinforced were there are long ranged correlation in the environment and that super diffusivity also occurs in higher dimensions.