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 |
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| 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 |
| 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. |
| Metadata Review: | All Records > Caltech Library Services |
| ID Code: | 3946 |
| Collection: | CaltechAUTHORS |
| Deposited By: | Lindsay Cleary |
| Deposited On: | 20 Jul 2006 |
| Last Modified: | 04 Jul 2008 20:23 |
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