From j.r.norris@statslab.cam.ac.uk Tue Jan 23 09:34:31 2001 Return-path: Envelope-to: g.r.grimmett@statslab.cam.ac.uk Delivery-date: Tue, 23 Jan 2001 09:34:31 +0000 Received: from solo.statslab.cam.ac.uk [131.111.20.38] (mail) by cougar.statslab.cam.ac.uk with esmtp (Exim 1.82 #2) id 14KzqQ-0004pU-00; Tue, 23 Jan 2001 09:34:30 +0000 Received: from james by solo.statslab.cam.ac.uk with local (Exim 3.12 #1 (Debian)) id 14KzqQ-0002cx-00; Tue, 23 Jan 2001 09:34:30 +0000 Subject: Seminar update To: Geoffrey Grimmett Date: Tue, 23 Jan 2001 09:34:30 +0000 (GMT) CC: James Norris X-Mailer: ELM [version 2.4ME+ PL66 (25)] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Message-Id: From: James Norris Status: RO Probability Seminars

Statistical Laboratory Seminars

Informal Probability Seminars

Lent Term 2001

All interested are encouraged to take part to the full by presenting their ideas and discussing those of others. Graduate students especially are urged to attend.

All talks will be in Meeting Room 12 of the Centre for Mathematical Sciences, Pavilion D. For directions to the Statistical Laboratory, see the Statistical Laboratory home web page. The Centre is reached by a path along the west side of the Isaac Newton Institute in Clarkson Road.

Tuesday 23 January

No seminar

Tuesday 30 January

2pm Nilanjana Datta

Excited state wavefunctions in the quantum transverse Ising model Abstract. Convergent expansions of the wavefunctions for the ground state and low-lying excited states of quantum transverse Ising systems are obtained. These expansions are employed to prove the existence of a non-zero spectral gap above the ground state.

Tuesday 6 February

2pm Hengqing Ye (Singapore)

Diffusion approximations of multiclass priority queueing networks

Abstract. We extend the work of Chen and Zhang (1999b) and establish a new sufficient condition for the existence of the (conventional) diffusion approximation for multiclass queueing networks under priority service disciplines. This sufficient condition relates to the weak stability of the fluid networks and the stability of the high priority classes of the fluid networks that correspond to the queueing networks under consideration. Using this sufficient condition, we prove the existence of the diffusion approximation for the last-buffer-first-served reentrant lines. We also study a three-station network example, and observe that the diffusion approximation may not exist, even if the ``proposed'' limiting semimartingale reflected Brownian motion (SRBM) exists.

Tuesday 13 February

2pm Michel Ledoux (Toulouse)

Hypercontractivity of Hamilton-Jacobi equations

Tuesday 27 February

2pm Mikhail Menshikov (Durham)

Random walks in random environment on trees

Abstract. We study random walks in a random environment on a regular, rooted, coloured tree. The asymptotic behaviour of the walks is classified for ergodicity/recurrence/transience in terms of the geometric properties of the matrix describing the random environment. The close connection between various problems on random walks in random environment and the so called multiplicative chaos martingale will be shown.

Tuesday 13 March

2pm Oliver Johnson

Information theoretic central limit theorems

Abstract. We present new results concerning information-theoretic convergence in the Central Limit Theorem. In joint work with Barron, we present a simplified proof, which also provides an explicit rate of convergence, using so-called Poincare inequalities. We also present techniques which can provide a proof in certain dependent cases, under either a Rosenblatt-style mixing condition, or for FKG systems.

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