*Tid:***30 maj 2005 kl 1615-1700 **

*Plats :***Seminarierummet 3733**, Institutionen för
matematik, KTH, Lindstedts väg 25, plan 7. Karta!

*Föredragshållare:***
Mikael Foghelin.
**

**Titel:** **
Collision probabilities between random vectors.
(Examensarbete)
**

**Sammanfattning:** *n* white and *m* black balls are thrown into *r* urns,
a collision
occurs when an urn contains balls of both colours. What is the
probability that collisions occur in *l* of the *r* urns? An
analytic expression for this probability based on combinatorics
is presented in a symmetric special case. Methods of
approximating and simulating this probability in cases where
the symmetry is broken are studied. Particularly the validity
of the Poisson approximation is carefully investigated. Finally
two examples are treated.