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arXiv · 1602.03054

Tutte's invariant approach for Brownian motion reflected in the quadrant

Sandro Franceschi·Kilian Raschel
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Abstract

We consider a Brownian motion with drift in the quarter plane with orthogonal reflection on the axes. The Laplace transform of its stationary distribution satisfies a functional equation, which is reminiscent from equations arising in the enumeration of (discrete) quadrant walks. We develop a Tutte's invariant approach to this continuous setting, and we obtain an explicit formula for the Laplace transform in terms of generalized Chebyshev polynomials.

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Sandro Franceschi, Kilian Raschel. 2016-02-09. Tutte's invariant approach for Brownian motion reflected in the quadrant. https://doi.org/10.1051/ps/2017006

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