Nonintersecting Brownian Excursions

By Craig A. Tracy, Harold Widom. 2006

78 citations recorded by the source corpus.

Author(s): Tracy, Craig A.; Widom, Harold | Abstract: We consider the process of $n$ Brownian excursions conditioned to be nonintersecting. We show the distribution functions for the top curve and the bottom curve are equal to Fredholm determinants whose kernel we give explicitly. In the simplest case, these determinants are expressible in terms of Painlev #x27;{e} V functions. We prove that as $n\to \infty$, the distributional limit of the bottom curve is the Bessel process with parameter 1/2. (This is the Bessel process associated with Dyson's Brownian motion.) We apply these results to study the expected area under the bottom and top curves.

Subfields: Finance, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/72a7f271e1e25d8219998c60d21d20c912a7e442

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Citations in the corpus

• Statistical mechanics of complex neural systems and high dimensional data (2013, background): “aximal eigenvalue of multiple correlated matrices, corresponding to the restriction of the same random projection to each plane. Thus results from the eigenvalue spectra of random correlated matrices [168, 169, 170] could become relevant. Finally, we note that throughout most of this review we have ”
• Brownian Gibbs property for Airy line ensembles (2011, background): “The ensemble of non-intersecting Brownian exclusions [78] also satisfies (H)k,T Theorem 3.”