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Dembo, Amir; Gantert, Nina; Zeitouni, Ofer

Large deviations for random walk in random environment with holding times. (English) Zbl 1126.60035

Ann. Probab. 32, No. 1B, 996-1029 (2004).
Summary: 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 \(\mathbb R_+\)), 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.

Cited in 5 Documents

MSC:

60G50 Sums of independent random variables; random walks
60F10 Large deviations
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60K37 Processes in random environments
82C41 Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics
82C44 Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics

Keywords:

random walk in random environment; large deviations; holding times
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References:

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