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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 774.60036

**Autor: ** Erdös, Paul; Révész, P.

**Title: ** Three problems on the random walk in Z^{d}. (In English)

**Source: ** Stud. Sci. Math. Hung. 26, No.2/3, 309-320 (1991).

**Review: ** A simple symmetric random walk in **Z**^{d} is considered. The following three functionals are studied and their asymptotic behaviour is analysed:

R_{d}(n): Largest integer for which there exists a random variable u such that all the points in the ball of radius R_{d}(n) centered at u are visited by time n (d \geq 3).

\nu_{d}(n): Time needed, after time n, to visit a point not previously visited.

f_{n}: Cardinality of the set of ``favourite values'', i.e. sites most often visited by time n.

**Reviewer: ** B.Bassan (Milano)

**Classif.: ** * 60F15 Strong limit theorems

60G50 Sums of independent random variables

00A07 Problem books

60J15 Random walk

**Keywords: ** symmetric random walk

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag