Random Walk Among Mobile/Immobile Traps: A Short Review

  • Siva Athreya
  • Alexander Drewitz
  • Rongfeng SunEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 300)


There have been extensive studies of a random walk among a field of immobile traps (or obstacles), where one is interested in the probability of survival as well as the law of the random walk conditioned on its survival up to time t. In contrast, very little is known when the traps are mobile. We will briefly review the literature on the trapping problem with immobile traps, and then review some recent results on a model with mobile traps, where the traps are represented by a Poisson system of independent random walks on \(\mathbb {Z}^d\). Some open questions will be given at the end.


Trapping problem Parabolic anderson model Random walk in random potential 



R.S. is supported by NUS grant R-146-000-220-112. S.A. is supported by CPDA grant and ISF-UGC project. We thank Ryoki Fukishima for helpful comments that corrected some earlier misstatements. Lastly, we thank Vladas Sidoravicius for encouraging us to write this review, and we are deeply saddened by his untimely death.


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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Indian Statistical InstituteBangaloreIndia
  2. 2.Mathematisches InstitutUniversität zu KölnKölnGermany
  3. 3.Department of MathematicsNational University of SingaporeSingaporeSingapore

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