The canonical time is Tuesday afternoon, but some talks are on other afternoons. 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.
The Lab has moved to the new Centre for Mathematical Sciences, where it now occupies Pavilion D. All talks will be in Meeting Room 12 of the new Laboratory, unless otherwise announced. For directions to the new 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.
Monday 25 September
2pm Senya Shlosman (Moscow, Marseille)
Statistical mechanics on hyperbolic graphs
Tuesday 17 October
2pm James Norris
Collapse of random hypergraphs
Tuesday 24 October
2pm Neil O'Connell (BRIMS)
The characteristic polynomial of a random unitary matrix
Tuesday 31 October
2pm Alexander Komech (Moscow)
Gaussian limit distributions for linear hyperbolic equations
Abstract. Consider the wave and Klein-Gordon equations in a Euclidean space. Assuming that the initial data are random, what can be said about the distribution of the solution to the Cauchy problem at a large time? This talk will focus on Gaussian limit theorems emerging within such approach. The audience is not required to have the preliminary knowledge of the theory of PDE's.
Tuesday 7 November
2pm Lane Hughston (Kings College, London)
Integral representations for bond price processes
Tuesday 14 November
2pm Geoffrey Grimmett
Directed percolation and random walk
The talk of Mikhail Menshikov on `Random walks in random environment on trees' has been postponed until next term, because of travel problems.
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.
Friday 17 November
2pm Mark Davis (Imperial College, London)
Optimal hedging with basis risk
Tuesday 21 November
2pm Dave Sheridan
Stein's Method in application to random matrices
We shall consider a sequence of random matrices M_n, chosen according to Haar measure from the (n x n) Unitary group. Let Xi_n be the empirical measure induced by the eigenvalues on M_n. That is, Xi_n is a measure composed of n atoms of unit mass on the unit circle (or equivalently, on [0,2pi]). We shall prove a Central Limit Theorem (CLT) for these measures as n->infinity, using Stein's method. In this lecture, I shall give a recap of Stein's method itself, followed by a suitable formulation for empirical measures. In particular, I shall make sense of the term "CLT" for measures. A very general CLT holds for empirical measures on the circle, requiring only a condition on moments. I shall then show that the Random Matrix case above is covered by the theorem and provide some discussion on why the Orthogonal and Symplectic groups are much more difficult to study.
Tuesday 28 November
2pm Matthew Donald (Cavendish Lab)
Quantum relative entropy/Kullback-Leibler information -- An overview for probabilists Relative entropy, or Kullback-Leibler information, is a valuable tool allowing one to determine how likely it is for one probability distribution to behave like another. In quantum theory, we work with states on von Neumann algebras which are generalizations of probability distributions. A relative entropy function with many useful properties can be defined in this general context. It has applications in quantum information theory and quantum statistical mechanics. The idea of determining how likely it is for one state to behave like another also generalizes and can be used to motivate axioms which characterize relative entropy. This provides a possible foundation for quantum probability in the context of local quantum field theory where the wave-functions and transition amplitudes of elementary quantum mechanics can no longer be considered as fundamental. The seminar will be a survey not assuming familiarity either with quantum theory or with von Neumann algebras.
to return to Geoffrey Grimmett's home page.