# Probability Theory & Its Applications

*by Various Speakers*

*Institution:*Various

*Date: Wed 20th March 2013*

*Time: 3:15 PM*

*Location: Lower Theatrette, Babel Building (a.k.a. Babel-G03), University of Melbourne*

*Abstract*: We are delighted to announce that the next traditional (the sixth in the series) UofM & Monash micro-conference on

Probability Theory & Its Applications

proudly supported by MASCOS will be held at the University of Melbourne on Wednesday, 20 March 2013 afternoon (15:15-18:05, so that there will be no clash with Davide Ferrari's SSAI talk starting @ Russell Love Theatre at 18:15).

There will be four 30+5' talks, to be followed by a dinner (18:45 +).

How to get there: Go to Babel Building @ Parkville Campus, Melbourne Uni (Bldg 139, square F3 on the Campus Map), enter from the main foyer and turn left.

++++++++++++++++++++ PROGRAM +++++++++++++++++++++

** 3:20-3:50pm [3:55 end of question time] Talk 1: Variance asymptotics for random polytopes in smooth convex bodies.

Speaker: Joe Yukich (Lehigh University)

** 3:55-4:25pm [4:30 end of question time] Talk 2: A revisit of approximate Melamed's theorem

Speaker: Aihua Xia (Melbourne Uni)

**4:30-5:00pm

Tea/coffee break (next to the theatrette)

** 5:00-5:30pm [5:35 end of question time] Talk 3: Large deviations for stochastic functional differential equations.

Speaker: Atsushi Takeuchi (Osaka City University)

** 5:35-6:05pm [6:10 end of question time] Talk 4: On Large deviations and interacting particles systems

Speaker: Andrea Collevecchio (Monash Uni)

** 6:45pm +

Dinner (venue TBA)

+++++++++++++++ END OF PROGRAM ++++++++++++++++++++

*For More Information:* Before providing more info on the event:

++ If you are going to come to the talks, please email me at kostya.borovkov@gmail.com -- we will

need that information for tea/coffee catering purposes.

++ Plus, please let me know if you will be joining us for dinner

(planned to start around 6:45pm, at a local restaurant -- most likely, at an Italian place @ Lygon Street, Carlton), as we need the headcount for booking. You partner would be more than welcome as well. (Just to be on the safe side: at the dinner, we will have to pay for ourselves, as usual).

RSVP by Thursday, 14 March 2013. Thanks!

+++++++++ APPENDIX: Abstracts of the talks ++++++++++++++

Talk 1: The Variance asymptotics for random polytopes in smooth convex bodies

Speaker: Joe Yukich (Lehigh University)

Abstract: Let $K \subset \R^d$ be a smooth convex set and let $\P_\lambda$ be a Poisson point process on $\R^d$ of intensity $\lambda$.

The convex hull of $\P_\lambda \cap K$ is a random convex polytope $K_\lambda$. As $\lambda \to \infty$, we show that the variance of the number of $k$-dimensional faces of $K_\lambda$, when properly scaled, converges to a scalar multiple of the affine surface area of $K$. Similar asymptotics hold for the variance of the number of $k$-dimensional faces for the convex hull of a binomial process in $K$. This is joint work with Pierre Calka.

Talk 2: A revisit of approximate Melamed's theorem

Speaker: Aihua Xia (Melbourne Uni)

Abstract: We demonstrate that the equilibrium customer flow process (ECFP) along the links in a Jackson queuing network is asymptotically a negative binomial process.

Our result provides a better alternative than the approximate Melamed's theorem proposed by Barbour and Brown (1996) that the ECFP process is approximately Poisson if the probability of customers travelling along the links more than once is very small.

Talk 3: Large deviations for stochastic functional differential equations.

Speaker: Atsushi Takeuchi (Osaka City University)

Abstract: Consider stochastic functional differential equations depending on past histories. We shall study the large deviations for the family of the solution process, and apply it to the asymptotic behavior of the density. The Malliavin calculus plays a crucial role in our argument.

Talk 4: On Large deviations and interacting particles systems

Speaker: Andrea Collevecchio (Monash Uni)

Abstract: We talk about general large deviations principles and analyze their application to few interacting particles systems. In particular we study a system of Bosons and express important

quantities related to this system in terms of variational formulas.