Electronic Communications in Probability

A Large Wiener Sausage from Crumbs

Omer Angel, Itai Benjamini, and Yuval Peres

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Abstract

Let $B(t)$ denote Brownian motion in $R^d$. It is a classical fact that for any Borel set $A$ in $R^d$, the volume $V_1(A)$ of the Wiener sausage $B[0,1]+A$ has nonzero expectation iff $A$ is nonpolar. We show that for any nonpolar $A$, the random variable $V_1(A)$ is unbounded.

Article information

Source
Electron. Commun. Probab., Volume 5 (2000), paper no. 7, 67-71.

Dates
Accepted: 24 April 2000
First available in Project Euclid: 2 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1456943500

Digital Object Identifier
doi:10.1214/ECP.v5-1019

Mathematical Reviews number (MathSciNet)
MR1781839

Zentralblatt MATH identifier
0951.60077

Subjects
Primary: 60J45: Probabilistic potential theory [See also 31Cxx, 31D05]
Secondary: 60J65: Brownian motion [See also 58J65] 31C15: Potentials and capacities

Keywords
Brownian motion capacity polar set Wiener sausage

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Angel, Omer; Benjamini, Itai; Peres, Yuval. A Large Wiener Sausage from Crumbs. Electron. Commun. Probab. 5 (2000), paper no. 7, 67--71. doi:10.1214/ECP.v5-1019. https://projecteuclid.org/euclid.ecp/1456943500


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References

  • I. Benjamini, R. Pemantle and Y. Peres (1995), Martin capacity for Markov chains. Ann. Probab. 23, 1332-1346.
  • K. Ito and H. P. McKean (1974), Diffusion Processes and Their Sample Paths, Second printing. Springer-Verlag.
  • F. Spitzer (1964), Electrostatic capacity, heat flow, and Brownian motion. Z. Wahrschein. Verw. Gebiete 3, 110–121.
  • A. S. Sznitman (1998), Brownian motion, Obstacles and Random Media. Springer Monographs in Mathematics. Springer-Verlag, Berlin.