Collision local time of transient random walks and intermediate phases in interacting stochastic systems
Birkner M, den Hollander F, Greven A (2011)
Publication Type: Journal article, Original article
Publication year: 2011
Journal
Publisher: Institute of Mathematical Statistics (IMS): OAJ / Institute of Mathematical Statistics
Book Volume: 16
Pages Range: 552-586
URI: https://projecteuclid.org/euclid.ejp/1464820189
Abstract
In a companion paper [6], a quenched large deviation principle (LDP) has been established for the empirical process of words obtained by cutting an i.i.d. sequence of letters into words according to a renewal process. We apply this LDP to prove that the radius of convergence of the generating function of the collision local time of two independent copies of a symmetric and strongly transient random walk on Zd, d ≥ 1, both starting from the origin, strictly increases when we condition on one of the random walks, both in discrete time and in continuous time. We conjecture that the same holds when the random walk is transient but not strongly transient. The presence of these gaps implies the existence of an intermediate phase for the long-time behaviour of a class of coupled branching processes, interacting diffusions, respectively, directed polymers in random environments.
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Germany (DE)
Netherlands (NL)How to cite
APA:
Birkner, M., den Hollander, F., & Greven, A. (2011). Collision local time of transient random walks and intermediate phases in interacting stochastic systems. Electronic Journal of Probability, 16, 552-586.
MLA:
Birkner, Matthias, Frank den Hollander, and Andreas Greven. "Collision local time of transient random walks and intermediate phases in interacting stochastic systems." Electronic Journal of Probability 16 (2011): 552-586.
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