Department of Mathematical Sciences

Dini's helix - a pseudospherical surface Brownian motion Willmore cylinder with umbilic lines
		   (Babich-Bobenko) Triadic Von Koch Snowflake - Fleckinger, Levitin
		   and Vassiliev Darboux transform of a Clifford torus (Holly
		   Bernstein) Mandelbrot fractal geometry

University of Bath - links to homepage University of Bath logo - links to University home

Admissions Teaching Postgraduates Research Staff News

Contact us

Alex Cox

Informal Probability Seminars: Spring 2008

Our seminars our usually held at 12.15 p.m. on Wednesdays in room 1W 3.6 . If you wish to find out more, please contact one of the organisers. The speakers are mostly internal (Bath) unless otherwise stated. Details of previous semesters can be found here

18/1/08: Max von Renesse(TU Berlin)

Particle Approximation of the Wasserstein Diffusion

The Wasserstein Diffusion is a special random process on the probability distributions on the unit interval which is closely related to the quadratic Wasserstein distance and whose unique invariant measure admits a formal Gibbs type representation with the relative entropy as Hamiltonian.
We review the initial construction by Dirichlet form methods first. In the second part of the talk we present an approximation by a sequence of interacting particle systems.

Note time and day: 11.15am, Friday

8/2/08: Olivier Zindy(WIAS)

Aging for random walks in random environment in the sub-ballistic regime

We consider transient one-dimensional random walks in random environment with zero asymptotic speed. An aging phenomenon involving the generalized Arcsine law is proved using the localization of the walk at the foot of `valleys' of height log t.

Note time and day: 10.15am, Friday

13/2/08: Pierre Patie (Bern)

Law of the exponential functional of a family of one-sided Lévy processes.

J. Bertoin and M. Yor determine the law of the exponential functional of a spectrally positive Lévy process with a negative mean through their negative entire moments. In this talk, we start by computing, in terms of new power series, the Laplace transform of such a functional associated to a spectrally negative Lévy process satisfying Rivero's condition. Then, specifying on a new family of one-sided Lévy processes, we provide an expression for the density of their corresponding exponential functionals in terms of the Wright hypergeometric functions. This is achieved by connecting such laws with the entrance laws of the family of self-similar continuous state branching processes with immigration. We end up by establishing some interesting analytical properties enjoyed by the Wright hypergeometric functions.

20/2/08: Peter Mörters

The local time of additive Levy processes in supercritical dimensions

26/2/08: Markus Heydenreich (TU/e)

Long-range percolation

I plan to introduce long-range percolation and review selected literature. I will discuss a recent result on mean-field behaviour of long-range percolation, obtained jointly with Remco van der Hofstad and Akira Sakai.

Note time and day: 11.15, Tuesday

27/2/08: Marcel Ortgiese

Small value probabilities via the branching tree heuristic

We present an easy and intuitive technique for calculating small value probabilities in a wide range of problems. Our primary example is the well-known small value problem for the martingale limit of a supercritical Galton-Watson process. But we will see that the same intuition also works in the quite different context of self-intersections of stochastic processes. For instance, it allows us to identify the small value probabilities for intersection local times of several Brownian motions, as well as for the self-intersection local times of a single Brownian motion.

10/3/08: Nikos Zygouras (USC)

Pinning-depinning transition in Random Polymers


Note time and day: 11.15, Monday

12/3/08: Janos Englander

An interacting spatial branching model - work in progress

I will try to share a couple of ideas with the audience about a spatial particle (branching) system with a simple interaction. We will also study how the center of mass behaves for certain spatial branching systems.

28/3/08: Jean Bertoin (Paris VI)

The structure of the allelic partition for Galton-Watson processes with neutral mutations

Note time and day: TBA, Friday

9/4/08: Julien Berestycki (Paris VI)

Kingman coalescent and Brownian excursion : some classical results revisited with an application to the multifractal spectrum of Kingman's coalecsent

It is a folk theorem to say that the genealogy of a Brownian excursion is given by Kingman's coalescent. Two important and well known results hint at this. Le Gall has shown that the genealogy of the Dawson-Watanabe superprocessus is encoded in the Brownian excursion while Perkins, in his so-called desintegration theorem, shows that a renormalized Dawson-Watanabe superprocessus is just a Flemming-Viot superprocessus whose genealogy is well known to be Kingman's coalescent. Here, we give an explicit embedding of Kingman's coalescent in the Brownian excursion which allows us to compute the multifractal spectrum of the coalescent. Those results complements an earlier joint work with N. Berestycki and J. Schweinsberg.

16/4/08: Loïc Chaumont (Angers)

Reflection principle and Ocone martingales

Let $M =(M_t)_{t\geq 0}$ be any continuous real-valued stochastic process. We prove that if there exists a sequence $(x_n)$ of real numbers which converges to 0 and such that $M$ satisfies the reflection property at all levels $x_n$ and $2x_n$, then $M$ is a local Ocone martingale. We state the subsequent open question: is this result still true when the property only holds at levels $x_n$~? Then we prove that the later question is equivalent to the fact that for Brownian motion, the sigma field of the invariant events by all the reflections at levels $x_n$, $n\ge1$ is trivial.

23/4/08: Stanislav Volkov

Random walks with time and space dependent drifts

We will consider a one-dimensional discrete-time stochastic process with asymptotically zero drift, which depends both on the time and the position of the walker. We establish an interesting phase transition of these walks, which cover a whole range of other models: from Lamperti's problem to Friedman's urn model. For the latter, we manage to answer an apparently still open question.
Based on a joint work with Mikhail Menshikov (Durham)

30/4/08: Mathew Penrose

Normal approximation in stochastic geometry via size-biased couplings

Consider n random points in a square of volume n, each surrounded by a unit disk. We discuss the rate of normal approximation for the number of isolated points, and for the amount of covered area.

14/5/08: Simon Harris

Inhomogenous branching Brownian motion : the perils of a quadratic potential

21/5/08: Vadim Shcherbakov

On a simple growth model

A simple spread/growth model will be defined. The asymptotic behaviour of the model has been studied in details in a special case (typical results will be given) and no results known (?) in a general case, which will be briefly discussed.

16/6/08: Ben Kaehler

Pricing American Rainbow Options and Multivariate Variance Gamma Processes

This talk is on two topics related to pricing American rainbow options using Lévy processes. An American rainbow option is an option on two or more underlying assets that can be exercised at any time before maturity. Pricing an American Rainbow option under the usual Black-Scholes assumptions becomes difficult in high dimensions due to the curse of dimensionality. A method for making those calculations tractable is discussed. Extending those results to a world where prices follow multivariate exponential Lévy processes requires additional assumptions about the processes. Some alternatives for generalising the successful Variance Gamma process into higher dimensions are presented for that purpose.

Note time and day: 11.15, Monday


Seminars will be added to this list as they are confirmed. Please check back for the latest list, or subscribe to the prob-sem mailing list to receive details of future seminars

Related Information

  • Subscribe to the prob-sem mailing list to receive details of future seminars