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A model for the bus system in Cuernavaca (Mexico)

Baik, Jinho and Borodin, Alexei and Deift, Percy and Suidan, Toufic (2006) A model for the bus system in Cuernavaca (Mexico). Journal of Physics A: Mathematical and General, 39 (28). pp. 8965-8975. ISSN 0305-4470. http://resolver.caltech.edu/CaltechAUTHORS:BAIjpa06

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Abstract

The bus system in Cuernavaca, Mexico and its connections to random matrix distributions have been the subject of an interesting recent study by M Krbálek and P Seba in [15, 16]. In this paper we introduce and analyse a microscopic model for the bus system. We show that introducing a natural repulsion does produce random matrix distributions in natural double scaling regimes. The techniques employed include non-intersecting paths, logarithmic potential theory, determinantal point processes, and asymptotic analysis of several orthogonal polynomial ensembles. In addition, we introduce a circular bus model and include various calculations of non-crossing probabilities.


Item Type:Article
Additional Information:© 2006 IOP Publishing Ltd. Received 19 October 2005, in final form, 17 January 2006; published 27 June 2006 online at stacks.iop.org/JPhysA/39/8965. The authors would like to thank Y Avron for bringing the work of Krbálek and Šeba to their attention. The authors would like to thank P Šeba and E Bachmat for providing useful information. The authors would also like to thank the anonymous referees for pointing out [9, 12] and improving the presentation. The work of the authors was supported in part by NSF grants DMS0457335, DMS0402047, DMS0296084/0500923 and DMS0202530/0553403, respectively.
Subject Keywords:EIGENVALUE CORRELATIONS; ORTHOGONAL POLYNOMIALS; EXPONENTIAL WEIGHTS; RANDOM MATRICES; UNIVERSALITY; ASYMPTOTICS; RESPECT
Issue or Number:28
Record Number:CaltechAUTHORS:BAIjpa06
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:BAIjpa06
Alternative URL:http://dx.doi.org/10.1088/0305-4470/39/28/S11
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3946
Collection:CaltechAUTHORS
Deposited By: Lindsay Cleary
Deposited On:20 Jul 2006
Last Modified:26 Dec 2012 08:57

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