Displaying similar documents to “Chevet type inequality and norms of submatrices”

Aging and quenched localization for one-dimensional random walks in random environment in the sub-ballistic regime

Nathanaël Enriquez, Christophe Sabot, Olivier Zindy (2009)

Bulletin de la Société Mathématique de France

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We consider transient one-dimensional random walks in a random environment with zero asymptotic speed. An aging phenomenon involving the generalized Arcsine law is proved using the localization of the walk at the foot of “valleys“ of height log t . In the quenched setting, we also sharply estimate the distribution of the walk at time t .

Semidirected random polymers: Strong disorder and localization

Nikolaos Zygouras (2010)

Actes des rencontres du CIRM

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Semi-directed, random polymers can be modeled by a simple random walk on Z d in a random potential - ( λ + β ω ( x ) ) x ∈ Z d , where λ > 0 , β > 0 and ω ( x ) x ∈ Z d is a collection of i.i.d., nonnegative random variables. We identify situations where the annealed and quenched costs, that the polymer pays to perform long crossings are different. In these situations we show that the polymer exhibits localization.

On the limiting empirical measure of eigenvalues of the sum of rank one matrices with log-concave distribution

A. Pajor, L. Pastur (2009)

Studia Mathematica

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We consider n × n real symmetric and hermitian random matrices Hₙ that are sums of a non-random matrix H ₙ ( 0 ) and of mₙ rank-one matrices determined by i.i.d. isotropic random vectors with log-concave probability law and real amplitudes. This is an analog of the setting of Marchenko and Pastur [Mat. Sb. 72 (1967)]. We prove that if mₙ/n → c ∈ [0,∞) as n → ∞, and the distribution of eigenvalues of H ₙ ( 0 ) and the distribution of amplitudes converge weakly, then the distribution of eigenvalues of...

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...

Further results on laws of large numbers for uncertain random variables

Feng Hu, Xiaoting Fu, Ziyi Qu, Zhaojun Zong (2023)

Kybernetika

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The uncertainty theory was founded by Baoding Liu to characterize uncertainty information represented by humans. Basing on uncertainty theory, Yuhan Liu created chance theory to describe the complex phenomenon, in which human uncertainty and random phenomenon coexist. In this paper, our aim is to derive some laws of large numbers (LLNs) for uncertain random variables. The first theorem proved the Etemadi type LLN for uncertain random variables being functions of pairwise independent...

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

Henryk Gacki (1996)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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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 ) + ∫ 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...

The proportional likelihood ratio order and applications.

Héctor M. Ramos Romero, Miguel Angel Sordo Díaz (2001)

Qüestiió

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In this paper, we introduce a new stochastic order between continuous non-negative random variables called the PLR (proportional likelihood ratio) order, which is closely related to the usual likelihood ratio order. The PLR order can be used to characterize random variables whose logarithms have log-concave (log-convex) densities. Many income random variables satisfy this property and they are said to have the IPLR (increasing proportional likelihood ratio) property (DPLR property)....

Slowdown estimates for ballistic random walk in random environment

Noam Berger (2012)

Journal of the European Mathematical Society

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We consider models of random walk in uniformly elliptic i.i.d. random environment in dimension greater than or equal to 4, satisfying a condition slightly weaker than the ballisticity condition ( T ' ) . We show that for every ϵ > 0 and n large enough, the annealed probability of linear slowdown is bounded from above by exp ( - ( log n ) d - ϵ ) . This bound almost matches the known lower bound of exp ( - C ( log n ) d ) , and significantly improves previously known upper bounds. As a corollary we provide almost sharp estimates for the quenched...

Random fixed points of increasing compact random maps

Ismat Beg (2001)

Archivum Mathematicum

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Let ( Ω , Σ ) be a measurable space, ( E , P ) be an ordered separable Banach space and let [ a , b ] be a nonempty order interval in E . It is shown that if f : Ω × [ a , b ] → E is an increasing compact random map such that a ≤ f ( ω , a ) and f ( ω , b ) ≤ b for each ω ∈ Ω then f possesses a minimal random fixed point α and a maximal random fixed point β .

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...