Subdiffusivity of a Random Walk Among a Poisson System of Moving Traps on \(\mathbb {Z}\)

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• 作者：Siva Athreya ; Alexander Drewitz…
• 关键词：Parabolic anderson model ; Random walk in random potential ; Trapping dynamics ; Subdiffusive ; Thin points of a random walk
• 刊名：Mathematical Physics, Analysis and Geometry
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：20
• 期：1
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Theoretical, Mathematical and Computational Physics; Analysis; Geometry; Group Theory and Generalizations; Applications of Mathematics;
• 出版者：Springer Netherlands
• ISSN：1572-9656
• 卷排序：20

文摘

We consider a random walk among a Poisson system of moving traps on \(\mathbb {Z}\). In earlier work (Drewitz et al. Springer Proc. Math. 11, 119-158 2012), the quenched and annealed survival probabilities of this random walk have been investigated. Here we study the path of the random walk conditioned on survival up to time t in the annealed case and show that it is subdiffusive. As a by-product, we obtain an upper bound on the number of so-called thin points of a one-dimensional random walk, as well as a bound on the total volume of the holes in the random walk’s range.