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We study the asymptotic behavior of the simple random walk on oriented versions of Z 2. The considered lattices are not directed on the vertical axis but unidirectional on the horizontal one, with random orientations whose distributions are generated by a dynamical system. We find a sufficient condition on the smoothness of the generation for the transience… (More)

The aim of this paper is to present a result of discrete approximation of some class of stable self-similar stationary increments processes. The properties of such processes were intensively investigated, but little is known on the context in which such processes can arise. To our knowledge, discretisation and convergence theorems are available only in the… (More)

We prove a non-standard functional limit theorem for a two dimensional simple random walk on some randomly oriented lattices. This random walk, already known to be transient, has different horizontal and vertical fluctuations leading to different normalizations in the functional limit theorem, with a non-Gaussian horizontal behavior. We also prove that the… (More)

We consider a stochastic version of the k-server problem in which k servers move on a circle to satisfy stochastically generated requests. The requests are independent and identically distributed according to an arbitrary distribution on a circle, which is either discrete or continuous. The cost of serving a request is the distance that a server needs to… (More)

Random walks in random scenery are processes defined by Zn := n k=1 ωS k where S := (S k , k ≥ 0) is a random walk evolving in Z d and ω := (ωx, x ∈ Z d) is a sequence of i.i.d. real random variables. Under suitable assumptions on the random walk S and the random scenery ω, almost surely with respect to ω, the correctly renormalized sequence (Zn) n≥1 is… (More)

Open Quantum Random Walks, as developed in [1], are the exact quantum generalization of Markov chains on finite graphs or on nets. These random walks are typically quantum in their behavior, step by step, but they seem to show up a rather classical asymptotic behavior , as opposed to the quantum random walks usually considered in Quantum Information Theory… (More)

- Nadine Guillotin-Plantard, Julien Poisat, Renato Soares dos Santos
- 2013

Random walks in random sceneries (RWRS) are simple examples of stochastic processes in disordered media. They were introduced at the end of the 70's by Kesten-Spitzer and Borodin, motivated by the construction of new self-similar processes with stationary increments. Two sources of randomness enter in their definition: a random field ξ = (ξ(x)) x∈Z d of… (More)

We study the asymptotic behavior of the simple random walk on oriented versions of Z 2. The considered lattices are not directed on the vertical axis but unidirectional on the horizontal one, with symmetric random orientations which are positively correlated. We prove that the simple random walk is transient and also prove a functional limit theorem in the… (More)

We present a (non-standard) probabilistic analysis of dynamic data structures whose sizes are considered dynamic random walks. The basic operations (insertion, deletion, positive and negative queries, batched insertion, lazy deletion, etc.) are time-dependent random variables. This model is a (small) step toward the analysis of these structures when the… (More)