Large Favourite Sites of Simple Random Walk and theWiener Process

Large Favourite Sites of Simple Random Walk and the Wiener Process Large Favourite Sites of Simple Random Walk and the Wiener Process

Let U (n) denote the most visited point by a simple symmetric random walk fS k g k0 in the rst n steps. It is known that U (n) and max 0kn S k satisfy the same law of the iterated logarithm, but have diierent upper functions (in the sense of P. L evy). The distance between them however turns out to be transient. In this paper, we establish the exact rate of escape of this distance. The correspo...

Favourite sites of simple random walk

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 Pál Erdős and Pál Révész in the early eighties.

Tied Favourite Edges for Simple Random Walk Bb Alint Tt Oth

We show that there are almost surely only nitely many times at which there are at least 4 `tied' favourite edges for a simple random walk. This (partially) answers a question of P. Erd} os and P. R ev esz.

Cut times for Simple Random Walk Cut times for Simple Random Walk

Let S(n) be a simple random walk taking values in Z d. A time n is called a cut time if S0; n] \ Sn + 1; 1) = ;: We show that in three dimensions the number of cut times less than n grows like n 1? where = d is the intersection exponent. As part of the proof we show that in two or three dimensions PfS0; n] \ Sn + 1; 2n] = ;g n ? ; where denotes that each side is bounded by a constant times the ...

Large Deviations for Random Walk in Random