Random Walks in a One-Dimensional Lévy Random Environment
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- 作者：Alessandra Bianchi ; Giampaolo Cristadoro ; Marco Lenci…
- 关键词：Levy walks ; RWRE ; Random walks on point processes ; Levy ; Lorentz gas ; Levy environment ; Central Limit theorem ; Convergence of moments
- 刊名：Journal of Statistical Physics
- 出版年：2016
- 出版时间：April 2016
- 年：2016
- 卷：163
- 期：1
- 页码：22-40
- 全文大小：562 KB
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Giampaolo Cristadoro (2)
Marco Lenci (2) (3)
Marilena Ligabò (4)
1. Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Trieste 63, 35121, Padova, Italy
2. Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40126, Bologna, Italy
3. Istituto Nazionale di Fisica Nucleare, Sezione di Bologna, Via Irnerio 46, 40126, Bologna, Italy
4. Dipartimento di Matematica, Università degli Studi di Bari, Via E. Orabona 4, 70125, Bari, Italy - 刊物类别：Physics and Astronomy
- 刊物主题：Physics
Statistical Physics
Mathematical and Computational Physics
Physical Chemistry
Quantum Physics - 出版者：Springer Netherlands
- ISSN：1572-9613
文摘
We consider a generalization of a one-dimensional stochastic process known in the physical literature as Lévy-Lorentz gas. The process describes the motion of a particle on the real line in the presence of a random array of marked points, whose nearest-neighbor distances are i.i.d. and long-tailed (with finite mean but possibly infinite variance). The motion is a continuous-time, constant-speed interpolation of a symmetric random walk on the marked points. We first study the quenched random walk on the point process, proving the CLT and the convergence of all the accordingly rescaled moments. Then we derive the quenched and annealed CLTs for the continuous-time process.