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math.PR2000
A signal-recovery system: asymptotic properties and construction of an infinite volume limit
Jacob van den Berg, Balint Toth
We consider a linear sequence of `nodes', each of which can be in state 0 (`off') or 1 (`on'). Signals from outside are sent to the rightmost node and travel instantaneously as far…
math.PR2000
Favourite sites of simple random walk
Zhan Shi, Balint Toth
We survey the current status of the list of questions related to the favourite (or: most visited) sites of simple random walk on Z, raised by Pal Erdos and Pal Revesz in the early…
math.PR2000
No more than three favourite sites for simple random walk
Balint Toth
We prove that, with probability one, eventually there are no more than three favourite (i.e. most visited) sites of simple random walk. This partially answers a relatively long sta…