Abstract
We study properties of occupation times by Brownian excursions and Brownian loops in two-dimensional domains. This allows for instance to interpret some Gaussian fields, such as the Gaussian Free Fields as (properly normalized) fluctuations of the total occupation time of a Poisson cloud of Brownian excursions when the intensity of the cloud goes to infinity.
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Acknowledgements
This paper is based on my Master’s thesis and was completed under the guidance of my supervisor Professor Wendelin Werner. The author acknowledges the support from a Fondation CFM-JP Aguilar grant.
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Wu, H. (2012). On the Occupation Times of Brownian Excursions and Brownian Loops. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLIV. Lecture Notes in Mathematics(), vol 2046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27461-9_7
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DOI: https://doi.org/10.1007/978-3-642-27461-9_7
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