10th World Congress in Probability and Statistics

Plenary Lectures

Plenary Mon-1

IMS Presidential Address

9:00 AM — 10:00 AM KST
Jul 18 Sun, 8:00 PM — 9:00 PM EDT

IMS Presidential Address

Regina Liu (Rutgers University), Susan Murphy (Harvard University)

This talk does not have an abstract.

Session Chair

Siva Athreya (Indian Statistical Institute) / Hee-Seok Oh (Seoul National University)

Plenary Mon-2

Wald Lecture 1 (Martin Barlow)

7:00 PM — 8:00 PM KST
Jul 19 Mon, 6:00 AM — 7:00 AM EDT

Random walks and fractal graphs

Martin Barlow (University of British Columbia)

This series of talks will study random walks on graphs with irregular, random or fractal structure. The motivation goes back to a 1976 article by the physicist Pierre de Gennes on percolation. Calling the simple random walk on a percolation cluster ‘the ant in the labyrinth’, he asked about its properties. It was conjectured in 1976, and has been proved in a number of cases since, that critical models in statistical physics have fractal structure.

I will review de Gennes' questions. Since random fractals are hard, a first step was to look at deterministic exact fractals, and the graphs that can be associated naturally with them. The simplest of these is the Sierpinski gasket graph (SGG), and I will start with this example. Early work in this area used direct probabilistic methods, which were often very specific to the particular graph. The search for a more robust theory leads one to look for more flexible tools, of which the first is given by the connection, between random walks and electrical networks.

Session Chair

Takashi Kumagai (Kyoto University)

Plenary Mon-3

Bernoulli Lecture (Allison Etheridge)

8:00 PM — 9:00 PM KST
Jul 19 Mon, 7:00 AM — 8:00 AM EDT

Some models of spatially distributed populations: the effect of crowding

Alison Etheridge (University of Oxford)

We consider some models of spatially distributed populations in which we take account of the effects of local crowding on both the number of offspring produced by individuals, and the chance that those offspring survive to maturity. In particular, we would like to understand the way in which ancestry of individuals that survive in such populations is affected by different responses to crowding. A special case would be a birth-death process with an additional logistic term controlling local population growth, but the novelty here is that we can also see an influence on the way in which mature individuals disperse.

As time permits, we will touch on work with lots of people including Tom Kurtz (Madison), Peter Ralph (Oregon), Ian Letter, Aaron Smith, and Terence Tsui (all Oxford).

Session Chair

Ellen Baake (Bielefeld University)

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