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Random walks with strongly inhomogeneous rates and singular diffusions: Convergence, localization and aging in one dimension. (English) Zbl 1015.60099

The paper extends the previous work [Probab. Theory Relat. Fields 115, No. 3, 417-443 (1999; Zbl 0954.60094)] on chaotic time dependence in a disordered spin system. Technically that refers to the study of localization in the one-dimensional random walk with random rates. The main result is a general convergence criterion for localizaton and aging functionals of diffusions and walks with nonrandom speed measures. The localization is related to the concept of aging, typical for out of equilibrium phenomena in spin-glasses.

MSC:

60K37 Processes in random environments
60G18 Self-similar stochastic processes
82C44 Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics

Citations:

Zbl 0954.60094
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References:

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