Nadine Guillotin-Plantard

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We study the asymptotic behavior of the simple random walk on oriented versions of Z2. 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)
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)
When the support of X1 is a subset of N , (Sn)n≥0 is called a renewal process. Each time the random walk is said to evolve in Z, it implies that the walk is truly d-dimensional, i.e. the linear space generated by the elements in the support of X1 is d-dimensional. Institut Camille Jordan, CNRS UMR 5208, Université de Lyon, Université Lyon 1, 43, Boulevard(More)
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∈Zd of(More)
Department of Informatics and System Sciences, Sapienza University of Rome, aris@dis.uniroma1.it Lab. de Mathématiques et Applications, Univ. de Poitiers, clement.dombry@math.univ-poitiers.fr Université de Lyon, Institut Camille Jordan, nadine.guillotin@univ-lyon1.fr Department of Informatics, Athens University of Economics & Business, yiannis@aueb.gr(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)
Random walks in random sceneries were introduced independently by Kesten and Spitzer [9] and by Borodin [3, 4]. Let S = (Sn)n≥0 be a random walk in Zd starting at 0, i.e., S0 = 0 and (Sn − Sn−1)n≥1 is a sequence of i.i.d. Zd-valued random variables. Let ξ = (ξx)x∈Zd be a field of i.i.d. real random variables independent of S. The field ξ is called the(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)