Probability Seminar, Statistical Laboratory

Probability Seminar, Statistical Laboratory

Tuesdays 2-3 pm, MR 12.
Organisers: Nathanaël Berestycki, Peter Friz, and Mike Tehranchi.

Easter 2009

Previous term

Date Speaker Title Notes
21 April. Nikos Zygouras (Warwick). Pinning-depinning transition in Random Polymers (abstract).
29 April. Paul Malliavin (Paris VI). Construction of a probability measure with a prescribed logarithmic derivative ; existence and uniqueness.2pm. Note unusual day, but standard room.
5 May No seminar today.
12 May Anastasia Papavasiliou (Warwick) Parameter Estimation for Rough Differential Equations (abstract)
19 May Steven Strogatz (Cornell). The mathematics of collective synchronization (abstract) (Rouse Ball Lecture). 12pm Room 3, Mill Lane lecture rooms.
19 May Pierre Tarres (Oxford). Brownian polymers (abstract) Unusual time 4pm
26 May
June 2 Brian Rider (Colorado) A diffusion description of the random matrix hard edge (abstract)
June 9

Abstracts

April 21. Abstract for the talk of Nikos Zygouras.

May 12th. Parameter Estimation for Rough Differential Equations

Abstract: My goal is to estimate unknown parameters in the vector field of a rough differential equation, when the expected signature for the driving force is known and we estimate the expected signature of the response by Monte Carlo averages.

I will introduce the "expected signature matching estimator" which extends the moment matching estimator and I will prove its consistency and asymptomatic normality, under the assumption that the vector field is polynomial. Finally, I will describe the polynomial system one needs to solve in order to compute this estimatior.

April 21. Abstract for the talk of Pierre Tarres. June 2. A diffusion description of the random matrix hard edge.

Abstract: With J. Ramirez and B. Virag we recently proved that the limiting soft edge eigenvalues of the general beta ensembles have laws shared by the spectral points of a certain random Schroedinger operator. After recalling this fact I'll prove there is a similar picture at the random matrix hard edge. That is, the small eigenvalues of sample covariance ensembles are described in terms of a (random) differential operator in the large dimensional limit. Via a Riccati transformation, there is a second description though the hitting distributions of a simple diffusion. The latter picture allows a proof of the anticipated transition between the hard and soft edge laws.