Jinho Baik et al 2006 J. Phys. A: Math. Gen. 39 8965 doi:10.1088/0305-4470/39/28/S11
Jinho Baik1, Alexei Borodin2, Percy Deift3 and Toufic Suidan4
Show affiliationsThe 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 Šeba 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.
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
02.50.-r Probability theory, stochastic processes, and statistics
62H10 Distribution of statistics
Issue 28 (14 July 2006)
Received 19 October 2005, in final form 17 January 2006
Published 27 June 2006
Jinho Baik et al 2006 J. Phys. A: Math. Gen. 39 8965