**IIMAS - FENOMEC
UNAM**

**
**

** Which
drift/diffusion formulas for velocity-jump processes? **

**Resumen:**

This talk examines a class of linear hyperbolic systems
which generalizes the Goldstein–Kac model to an arbitrary
finite number of speeds with transition rates. Under the basic
assumptions that the transition matrix is symmetric and
irreducible, and the speed differences generate all the space,
the system exhibits a large-time behavior described by a
parabolic advection–diffusion equation. The main contribution
is to determine explicit formulas for the asymptotic drift
speed and diffusion matrix in term of the kinetic parameters,
establishing a complete connection between microscopic and
macroscopic coefficients. It is shown that the drift speed is
the arithmetic mean of the velocities. The diffusion matrix
has a more complicate representation, based on the graph with
vertices the velocities and arcs weighted by the transition
rates. The approach is based on an exhaustive analysis of the
dispersion relation and on the application of a variant of the
Kirchhoff’s matrix tree Theorem from graph theory.

17:00 hrs.

Salón 203, Edificio Anexo, IIMAS

Informes: coloquiomym@gmail.com, o al 5622-3564.