# Journal Club du LPTMS: Pierpaolo Vivo

## Pierpaolo Vivo, CNRS researcher LPTMS

### The statistical properties of the city transport in Cuernavaca (Mexico) and random matrix ensembles

I present the results of the two papers listed below on an interesting real-life system, namely the bus transportation in the Mexican city of Cuernavaca. In Cuernavaca there is no covering company responsible for organizing the city transport. Consequently, constraints such as a time table that represents external influence on the transport do not exist. Moreover, each bus is the property of the driver. The drivers try to maximize their income and hence the number of passengers they transport. This leads to competition among the drivers and to their mutual interaction. In the paper (1) below, the statistics of empirical inter-arrivals of buses was found to conform to the spacing distribution of Gaussian Unitary Ensemble (GUE) of random matrices. In the paper (2), a simple but rich model of self-avoiding walks with Poissonian rates is put forward to explain the empirical data, whose connection with GUE can be then analytically elucidated.

References:

1. M. Krbalek and P. Seba, The statistical properties of the city transport in Cuernavaca (Mexico) and random matrix ensembles, J. Phys. A: Math. Gen. 33, L229 (2000)

2. J. Baik, A. Borodin, P. Deift and T. Suidan, A model for the bus system in Cuernavaca (Mexico), J. Phys. A: Math. Gen. 39, 8965 (2006)

**Date/Time : ** 18/03/2013 - *12:00 - 12:45*

**Location : ** LPTMS, salle 201, 2ème étage, Bât 100, Campus d'Orsay

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