The probability that a one dimensional excited random walk in stationary ergodic and elliptic cookie environment is transient to the right (left) is either zero or one. This solves a problem posed by Kosygina and Zerner (Bull. Inst. Math. Acad. Sin. (N.S.) 8 (2013) 105-157). As an application, a law of large numbers holds in these conditions.
Amir, G., Berger, N., Orenshtein, T. (2016). Zero-one law for directional transience of one dimensional excited random walks. ANNALES DE L'INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 52(1), 47-57 [10.1214/14-AIHP615].
Zero-one law for directional transience of one dimensional excited random walks
Orenshtein T.
2016
Abstract
The probability that a one dimensional excited random walk in stationary ergodic and elliptic cookie environment is transient to the right (left) is either zero or one. This solves a problem posed by Kosygina and Zerner (Bull. Inst. Math. Acad. Sin. (N.S.) 8 (2013) 105-157). As an application, a law of large numbers holds in these conditions.
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