arvind singh - Academia.edu (original) (raw)
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Papers by arvind singh
We consider a one-dimensional transient cookie random walk. It is known from a previous paper [3]... more We consider a one-dimensional transient cookie random walk. It is known from a previous paper [3] that a cookie random walk (X n ) has positive or zero speed according to some positive parameter α > 1 or ≤ 1. In this article, we give the exact rate of growth of (X n ) in the zero speed regime, namely: for 0 < α < 1, X n /n α+1 2 converges in law to a Mittag-Leffler distribution whereas for α = 1, X n (log n)/n converges in probability to some positive constant .
Probability Theory and Related Fields, 2008
We consider the model of the one-dimensional cookie random walk when the initial cookie distribut... more We consider the model of the one-dimensional cookie random walk when the initial cookie distribution is spatially uniform and the number of cookies per site is finite. We give a criterion to decide whether the limiting speed of the walk is non-zero. In particular, we show that a positive speed may be obtained for just 3 cookies per site. We also prove a result on the continuity of the speed with respect to the initial cookie distribution.
We consider a one-dimensional transient cookie random walk. It is known from a previous paper [3]... more We consider a one-dimensional transient cookie random walk. It is known from a previous paper [3] that a cookie random walk (X n ) has positive or zero speed according to some positive parameter α > 1 or ≤ 1. In this article, we give the exact rate of growth of (X n ) in the zero speed regime, namely: for 0 < α < 1, X n /n α+1 2 converges in law to a Mittag-Leffler distribution whereas for α = 1, X n (log n)/n converges in probability to some positive constant .
Probability Theory and Related Fields, 2008
We consider the model of the one-dimensional cookie random walk when the initial cookie distribut... more We consider the model of the one-dimensional cookie random walk when the initial cookie distribution is spatially uniform and the number of cookies per site is finite. We give a criterion to decide whether the limiting speed of the walk is non-zero. In particular, we show that a positive speed may be obtained for just 3 cookies per site. We also prove a result on the continuity of the speed with respect to the initial cookie distribution.