Seminario Modelamiento Estocástico: “A Random Process of Tessellations that are Stable under Iterations (STIT)“

Lugar: Sala Multimedia, Sexto Piso, Centro de Modelamiento Matemático, Blanco Encalada 2120.

Fecha: Jueves 11 de marzo a las 17:00 hrs.

Expositor: Werner Nagel, (Universidad de Jena, Alemania).

Resumen: We consider random tessellations (mosaics) of the Euclidean space which are generated by sequential cell division. This yields a stochastic process (with discrete or continuous time) where the state space is a set of tessellations. There are several models of this type in the literature, but most of them are mathematically not feasible until now.

One particular model which is at least mathematically interesting is that of homogeneous STIT tessellations. In this model the random lifetimes of the cells until division are tuned in such a way that – at any time – the resulting tessellation is stochastically stable under the operation of iteration or nesting (defined for tessellations). This stability allows an elegant derivation of a series of results that are typical of stochastic geometry.

A further and promising step is a thorough study of the Markov process of these STIT tessellation. Some basic properties and recent results by Schreiber and Thaele can already be presented.

Contacto: mrivera@dim.uchile.cl

Organiza: Centro de Modelamiento Matemático, CMM.

Más información en: www.cmm.uchile.cl