**UM Math Graduate Students Seminar**

Dr. Daniel A. Díaz Pachón

*University of Miami*

**will present**

**Allocations: what they are and some open problems**

Friday, March 30, 2012, 4:00pm

Ungar Building Room 402

**Abstract:**Point processes are a probabilistic tool used in several fields of science (astronomy, particle motion, survival analysis, etc.) When analyzing (stationary) point processes, it is often useful to do it from the perspective of a "typical" point in the process. Although it is easy to do when there are finitely many points (one is chosen uniformly at random), the selection is very difficult when there are infinitely many points to be considered. In order to do so, we usually take the Palm version of the point process Z —i.e., a process Z' with the same law of Z conditioned to have a point in the origin— to select the origin as "typical". Allocations provide a way to translate Z in such a way that the translated process will have the law of Z'. In this talk, we analyze several of these allocations, their interesting graphical representations and some open problems.

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