The Annals of Probability

A Vervaat-like path transformation for the reflected brownian bridge conditioned on its local time at 0

Philippe Chassaing and Svante Janson

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We describe a Vervaat-like path transformation for the reflected Brownian bridge conditioned on its local time at 0: up to random shifts, this process equals the two processes constructed froma Brownian bridge and a Brownian excursion by adding a drift and then taking the excursions over the current minimum. As a consequence, these three processes have the same occupation measure, which is easily found.

The three processes arise as limits, in three different ways, of profiles associated to hashing with linear probing, or, equivalently, to parking functions.

Article information

Ann. Probab., Volume 29, Number 4 (2001), 1755-1779.

First available in Project Euclid: 5 March 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J65: Brownian motion [See also 58J65]
Secondary: 60C05: Combinatorial probability 68P10: Searching and sorting 68R05: Combinatorics

Brownian bridge Brownian excursion local time path transformation profile parking functions hashing with linear probing


Chassaing, Philippe; Janson, Svante. A Vervaat-like path transformation for the reflected brownian bridge conditioned on its local time at 0. Ann. Probab. 29 (2001), no. 4, 1755--1779. doi:10.1214/aop/1015345771.

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