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

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.

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Article dans une revue
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https://hal.univ-angers.fr/hal-03031592
Contributeur : Okina Université d'Angers <>
Soumis le : lundi 30 novembre 2020 - 15:20:25
Dernière modification le : mardi 1 décembre 2020 - 03:25:54

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  • HAL Id : hal-03031592, version 1
  • OKINA : ua79

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Citation

Marco Bertola, Mattia Cafasso. The Transition between the Gap Probabilities from the Pearcey to the Airy Process — a Riemann–Hilbert Approach. International Mathematics Research Notices, 2012, 2012 (7), pp.1519 - 1568. ⟨hal-03031592⟩

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