Abstract.
We present discrete schemes for processes in random media. We prove two results. The first one is the convergence of Sinai's random walks in random environments to the Brox model. The second one is the convergence of random walks in media with random “gates” to a continuous process in a Poisson potential. The proofs are based on the following idea: we consider the discrete media as random potentials for continuous models.
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Received: 6 May 1999 / Revised version: 18 October 1999 / Published online: 20 October 2000
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Seignourel, P. Discrete schemes for processes in random media. Probab Theory Relat Fields 118, 293–322 (2000). https://doi.org/10.1007/PL00008743
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DOI: https://doi.org/10.1007/PL00008743
Keywords
- Continuous Model
- Continuous Process
- Discrete Scheme
- Random Environment
- Random Medium