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January 2004 Large deviations for random walk in random environment with holding times
Amir Dembo, Nina Gantert, Ofer Zeitouni
Ann. Probab. 32(1B): 996-1029 (January 2004). DOI: 10.1214/aop/1079021470


Suppose that the integers are assigned the random variables $\{\omega_x,\mu_x\}$ (taking values in the unit interval times the space of probability measures on $\reals_+$), which serve as an environment. This environment defines a random walk $\{X_t\}$ (called a RWREH) which, when at x, waits a random time distributed according to $\mu_x$ and then, after one unit of time, moves one step to the right with probability $\omega_x$, and one step to the left with probability $1-\omega_x$. We prove large deviation principles for $X_t/t$, both quenched (i.e., conditional upon the environment), with deterministic rate function, and annealed (i.e., averaged over the environment). As an application, we show that for random walks on Galton--Watson trees, quenched and annealed rate functions along a ray differ.


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Amir Dembo. Nina Gantert. Ofer Zeitouni. "Large deviations for random walk in random environment with holding times." Ann. Probab. 32 (1B) 996 - 1029, January 2004.


Published: January 2004
First available in Project Euclid: 11 March 2004

zbMATH: 1126.60035
MathSciNet: MR2044672
Digital Object Identifier: 10.1214/aop/1079021470

Primary: 60F10 , 60J15 , 60J80 , 82C44

Keywords: holding times , large deviations , Random walk in random environment

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 1B • January 2004
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