### Abstract

Original language | English |
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Place of Publication | Eindhoven |

Publisher | Eurandom |

Number of pages | 29 |

Publication status | Published - 2010 |

### Publication series

Name | Report Eurandom |
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Volume | 2010016 |

ISSN (Print) | 1389-2355 |

### Fingerprint

### Cite this

*Collision local time of transient random walks and intermediate phases in interacting stochastic systems*. (Report Eurandom; Vol. 2010016). Eindhoven: Eurandom.

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*Collision local time of transient random walks and intermediate phases in interacting stochastic systems*. Report Eurandom, vol. 2010016, Eurandom, Eindhoven.

**Collision local time of transient random walks and intermediate phases in interacting stochastic systems.** / Birkner, M.; Greven, A.; Hollander, den, W.Th.F.

Research output: Book/Report › Report › Academic

TY - BOOK

T1 - Collision local time of transient random walks and intermediate phases in interacting stochastic systems

AU - Birkner, M.

AU - Greven, A.

AU - Hollander, den, W.Th.F.

PY - 2010

Y1 - 2010

N2 - In a companion paper, 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 moment 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.

AB - In a companion paper, 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 moment 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.

M3 - Report

T3 - Report Eurandom

BT - Collision local time of transient random walks and intermediate phases in interacting stochastic systems

PB - Eurandom

CY - Eindhoven

ER -