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Limits of detenninantal processes near a tacnode

Borodin, Alexei and Duits, Maurice (2011) Limits of detenninantal processes near a tacnode. Annales De l'Institut Henri Poincaré - Probabilitiés et Statistiques, 47 (1). pp. 243-258. ISSN 0246-0203.

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We study a Markov process on a system of interlacing particles. At large times the particles fill a domain that depends on a parameter ε > 0. The domain has two cusps, one pointing up and one pointing down. In the limit ε ↓ 0 the cusps touch, thus forming a tacnode. The main result of the paper is a derivation of the local correlation kernel around the tacnode in the transition regime ε ↓ 0. We also prove that the local process interpolates between the Pearcey process and the GUE minor process.

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Additional Information:© 2011 Association des Publications de l'Institute Henri Poincaré. Received 5 December 2009: revised 15 April 2010; accepted 26 April 2010.
Subject Keywords:Determinantal point processes: Random growth; GUE minor process: Pearcey process
Issue or Number:1
Classification Code:MSC: 82C22; 60K35; 6oG55
Record Number:CaltechAUTHORS:20110526-104843778
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Official Citation:Limits of determinantal processes near a tacnode Alexei Borodin and Maurice Duits; 243-258
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:23808
Deposited By: Ruth Sustaita
Deposited On:26 May 2011 18:20
Last Modified:03 Oct 2019 02:50

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