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The Transition between the Gap Probabilities from the Pearcey to the Airy Process—a Riemann–Hilbert Approach

Title:

The Transition between the Gap Probabilities from the Pearcey to the Airy Process—a Riemann–Hilbert Approach

Bertola, Marco and Cafasso, M. (2012) The Transition between the Gap Probabilities from the Pearcey to the Airy Process—a Riemann–Hilbert Approach. IMRN: International Mathematics Research Notices, 2012 (7). pp. 1519-1568. ISSN 1687-0247

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Official URL: http://imrn.oxfordjournals.org/content/2012/7/1519

Abstract

We consider the gap probability for the Pearcey and Airy processes; we set up a Riemann–Hilbert approach (different from the standard one) whereby the asymptotic analysis for large gap/large time of the Pearcey process is shown to factorize into two independent Airy processes using the Deift–Zhou steepest descent analysis. Additionally, we relate the theory of Fredholm determinants of integrable kernels and the theory of isomonodromic tau function. Using the Riemann–Hilbert problem mentioned above, we construct a suitable Lax pair formalism for the Pearcey gap probability and re-derive the two nonlinear PDEs recently found and additionally find a third one not reducible to those.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Article
Refereed:Yes
Authors:Bertola, Marco and Cafasso, M.
Journal or Publication:IMRN: International Mathematics Research Notices
Date:2012
ID Code:976936
Deposited By: DANIELLE DENNIE
Deposited On:05 Mar 2013 16:07
Last Modified:18 Jan 2018 17:43
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