共查询到20条相似文献,搜索用时 11 毫秒
1.
We consider random walk with a nonzero bias to the right, on the infinite cluster in the following percolation model: take i.i.d. bond percolation with retention parameter p on the so-called infinite ladder, and condition on the event of having a bi-infinite path from −∞ to ∞. The random walk is shown to be transient, and to have an asymptotic speed to the right which is strictly positive or zero depending on whether the bias is below or above a certain critical value which we compute explicitly. 相似文献
2.
Wolfgang König 《Probability Theory and Related Fields》1993,96(4):521-543
Summary We prove that a self-avoiding random walk on the integers with bounded increments grows linearly. We characterize its drift in terms of the Frobenius eigenvalue of a certain one parameter family of primitive matrices. As an important tool, we express the local times as a two-block functional of a certain Markov chain, which is of independent interest. 相似文献
3.
4.
Nina Gantert Zhan Shi 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2007,43(1):47
Let (Zn)n∈N be a d-dimensional random walk in random scenery, i.e., with (Sk)k∈N0 a random walk in Zd and (Y(z))z∈Zd an i.i.d. scenery, independent of the walk. The walker's steps have mean zero and some finite exponential moments. We identify the speed and the rate of the logarithmic decay of for various choices of sequences n(bn) in [1,∞). Depending on n(bn) and the upper tails of the scenery, we identify different regimes for the speed of decay and different variational formulas for the rate functions. In contrast to recent work [A. Asselah, F. Castell, Large deviations for Brownian motion in a random scenery, Probab. Theory Related Fields 126 (2003) 497-527] by A. Asselah and F. Castell, we consider sceneries unbounded to infinity. It turns out that there are interesting connections to large deviation properties of self-intersections of the walk, which have been studied recently by X. Chen [X. Chen, Exponential asymptotics and law of the iterated logarithm for intersection local times of random walks, Ann. Probab. 32 (4) 2004]. 相似文献
5.
Amine Asselah Fabienne Castell 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2007,43(2):163
We consider a random walk in random scenery {Xn=η(S0)+?+η(Sn),n∈N}, where a centered walk {Sn,n∈N} is independent of the scenery {η(x),x∈Zd}, consisting of symmetric i.i.d. with tail distribution P(η(x)>t)∼exp(−cαtα), with 1?α<d/2. We study the probability, when averaged over both randomness, that {Xn>ny} for y>0, and n large. In this note, we show that the large deviation estimate is of order exp(−ca(ny)), with a=α/(α+1). 相似文献
6.
Wolfgang König 《Probability Theory and Related Fields》1994,100(4):513-544
Summary Consider a one-dimensional walk (S
k
)
k
having steps of bounded size, and weight the probability of the path with some factor 1–(0,1) for every single self-intersection up to timen. We prove thatS
n
/S
S converges towards some deterministic number called the effective drift of the self-repellent walk. Furthermore, this drift is shown to tend to the basic drift as tends to 0 and, as tends to 1, to the self-avoiding walk's drift which is introduced in [10]. The main tool of the present paper is a representation of the sequence of the local times as a functional of a certain Markov process.Partially supported by Swiss National Sciences Foundation Grant 20-36305.92 相似文献
7.
We study models of discrete-time, symmetric, Zd-valued random walks in random environments, driven by a field of i.i.d. random nearest-neighbor conductances ωxy∈[0,1], with polynomial tail near 0 with exponent γ>0. We first prove for all d≥5 that the return probability shows an anomalous decay (non-Gaussian) that approaches (up to sub-polynomial terms) a random constant times n−2 when we push the power γ to zero. In contrast, we prove that the heat-kernel decay is as close as we want, in a logarithmic sense, to the standard decay n−d/2 for large values of the parameter γ. 相似文献
8.
Francis Comets Mikael Falconnet Oleg Loukianov Dasha Loukianova Catherine Matias 《Stochastic Processes and their Applications》2014
We consider a one dimensional ballistic random walk evolving in an i.i.d. parametric random environment. We provide a maximum likelihood estimation procedure of the parameters based on a single observation of the path till the time it reaches a distant site, and prove that the estimator is consistent as the distant site tends to infinity. Our main tool consists in using the link between random walks and branching processes in random environments and explicitly characterising the limiting distribution of the process that arises. We also explore the numerical performance of our estimation procedure. 相似文献
9.
We study the asymptotic behaviour of Markov chains (Xn,ηn) on Z+×S, where Z+ is the non-negative integers and S is a finite set. Neither coordinate is assumed to be Markov. We assume a moments bound on the jumps of Xn, and that, roughly speaking, ηn is close to being Markov when Xn is large. This departure from much of the literature, which assumes that ηn is itself a Markov chain, enables us to probe precisely the recurrence phase transitions by assuming asymptotically zero drift for Xn given ηn. We give a recurrence classification in terms of increment moment parameters for Xn and the stationary distribution for the large- X limit of ηn. In the null case we also provide a weak convergence result, which demonstrates a form of asymptotic independence between Xn (rescaled) and ηn. Our results can be seen as generalizations of Lamperti’s results for non-homogeneous random walks on Z+ (the case where S is a singleton). Motivation arises from modulated queues or processes with hidden variables where ηn tracks an internal state of the system. 相似文献
10.
Chunmao Huang Quansheng Liu 《Stochastic Processes and their Applications》2012,122(2):522-545
Let (Zn) be a supercritical branching process in a random environment ξ, and W be the limit of the normalized population size Zn/E[Zn|ξ]. We show large and moderate deviation principles for the sequence logZn (with appropriate normalization). For the proof, we calculate the critical value for the existence of harmonic moments of W, and show an equivalence for all the moments of Zn. Central limit theorems on W−Wn and logZn are also established. 相似文献
11.
We investigate the cumulative scenery process associated with random walks in independent, identically distributed random sceneries under the assumption that the scenery variables satisfy Cramér’s condition. We prove moderate deviation principles in dimensions d≥2, covering all those regimes where rate and speed do not depend on the actual distribution of the scenery. For the case d≥4 we even obtain precise asymptotics for the probability of a moderate deviation, extending a classical central limit theorem of Kesten and Spitzer. For d≥3, an important ingredient in the proofs are new concentration inequalities for self-intersection local times of random walks, which are of independent interest, whilst for d=2 we use a recent moderate deviation result for self-intersection local times, which is due to Bass, Chen and Rosen. 相似文献
12.
Eric David Belsley 《Probability Theory and Related Fields》1998,112(4):493-533
When run on any non-bipartite q-distance regular graph from a family containing graphs of arbitrarily large diameter d, we show that d steps are necessary and sufficient to drive simple random walk to the uniform distribution in total variation distance, and
that a sharp cutoff phenomenon occurs. For most examples, we determine the set on which the variation distance is achieved,
and the precise rate at which it decays.
The upper bound argument uses spectral methods – combining the usual Cauchy-Schwarz bound on variation distance with a bound
on the tail probability of a first-hitting time, derived from its generating function.
Received: 2 April 1997 / Revised version: 10 May 1998 相似文献
13.
Agoston Pisztora Tobias Povel Ofer Zeitouni 《Probability Theory and Related Fields》1999,113(2):191-219
ωx } (taking values in the interval [1/2, 1)), which serve as an environment. This environment defines a random walk {X k } (called a RWRE) which, when at x, moves one step to the right with probability ω x , and one step to the left with probability 1 −ωx. Solomon (1975) determined the almost-sure asymptotic speed (= rate of escape) of a RWRE, in a more general set-up. Dembo, Peres and Zeitouni (1996), following earlier work by Greven and den Hollander (1994) on the quenched case, have computed rough tail asymptotics for the empirical mean of the annealed RWRE. They conjectured the form of the rate function in a full LDP. We prove in this paper their conjecture. The proof is based on a “coarse graining scheme” together with comparison techniques. Received: 22 July 1997/Revised version: 15 June 1998 相似文献
14.
Burgess Davis 《Probability Theory and Related Fields》1999,113(4):501-518
Let b
t
be Brownian motion. We show there is a unique adapted process x
t
which satisfies dx
t
= db
t
except when x
t
is at a maximum or a minimum, when it receives a push, the magnitudes and directions of the pushes being the parameters of
the process. For some ranges of the parameters this is already known. We show that if a random walk close to b
t
is perturbed properly, its paths are close to those of x
t
.
Received: 15 October 1997 / Revised version: 18 May 1998 相似文献
15.
For a supercritical branching process (Zn) in a stationary and ergodic environment ξ, we study the rate of convergence of the normalized population Wn=Zn/E[Zn|ξ] to its limit W∞: we show a central limit theorem for W∞−Wn with suitable normalization and derive a Berry-Esseen bound for the rate of convergence in the central limit theorem when the environment is independent and identically distributed. Similar results are also shown for Wn+k−Wn for each fixed k∈N∗. 相似文献
16.
This article investigates the effect for random pinning models of long range power-law decaying correlations in the environment. For a particular type of environment based on a renewal construction, we are able to sharply describe the phase transition from the delocalized phase to the localized one, giving the critical exponent for the (quenched) free-energy, and proving that at the critical point the trajectories are fully delocalized. These results contrast with what happens both for the pure model (i.e., without disorder) and for the widely studied case of i.i.d. disorder, where the relevance or irrelevance of disorder on the critical properties is decided via the so-called Harris Criterion (Harris, 1974) [21]. 相似文献
17.
David Steinsaltz 《Probability Theory and Related Fields》1997,107(1):99-121
Summary. A self-modifying random walk on is derived from an ordinary random walk on the integers by interpolating a new vertex into each edge as it is crossed. This
process converges almost surely to a random variable which is totally singular with respect to Lebesgue measure, and which
is supported on a subset of having Hausdorff dimension less than , which we calculate by a theorem of Billingsley. By generating function techniques we then calculate the exponential rate
of convergence of the process to its limit point, which may be taken as a bound for the convergence of the measure in the
Wasserstein metric. We describe how the process may viewed as a random walk on the space of monotone piecewise linear functions,
where moves are taken by successive compositions with a randomly chosen such function.
Received: 20 November 1995 / In revised form: 14 May 1996 相似文献
18.
N. U. Prabhu 《Acta Appl Math》1994,34(1-2):213-223
A theory of semiregenerative phenomena was developed by the author. The set of points at which such a phenomenon occurs is called a semi regenerative set. There is a correspondence between a semiregenerative set and the range of a Markov subordinator with a unit drift (or a Markov renewal process in the discrete time case). Prabhu, Tang, and Zhu showed that the properties of semiregenerative sets associated with Markov random walks completely characterize the fluctuation behaviour of these processes in the nondegenerate case and also established a Wiener-Hopf factorization based on these sets. These results are surveyed in this paper. 相似文献
19.
20.
We study the random walk in a random environment on Z+={0,1,2,…}, where the environment is subject to a vanishing (random) perturbation. The two particular cases that we consider are: (i) a random walk in a random environment perturbed from Sinai’s regime; (ii) a simple random walk with a random perturbation. We give almost sure results on how far the random walker is from the origin, for almost every environment. We give both upper and lower almost sure bounds. These bounds are of order (logt)β, for β∈(1,∞), depending on the perturbation. In addition, in the ergodic cases, we give results on the rate of decay of the stationary distribution. 相似文献