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Published July 14, 2006 | public
Journal Article Open

A model for the bus system in Cuernavaca (Mexico)

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.

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.

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