Harry Kesten's 80th birthday

Sunday 20 November 2011
Malott Hall 406, Cornell University

Accommodation and Dinner

Rooms are being held at the Holiday Inn, Ithaca, and participants are invited to make their own reservations.
A special rate of $129 + tax is available on quoting “Harry Kesten Conference”.

There will be a special dinner for Harry after the lectures on 20 November. Please email Geoffrey Grimmett as soon as possible if you wish to attend. Places are limited, and it may not be possible to accommodate people who give insufficient notice.


10.30–10.45 Laurent Saloff-Coste, Cornell University
10.45–11.30 Vladas Sidoravicius, IMPA (Chair: LSC)
Percolation of words
11.30–12.15 Hugo Duminil-Copin, Geneva University
Near-critical random-cluster model: beyond the pivotal sites phenomenon
In 1980, Kesten proved that the critical value of bond percolation on the square lattice equals 1/2. The proof harnessed a clever estimation of the number of pivotal sites for crossing events. It enabled the study of the probability of these crossing events with respect to the edge-parameter p. Seven years later, Kesten rigorously proved a relation between the probability of being pivotal and the so-called correlation length of percolation. We shall discuss similar questions in random-cluster models on the square lattice.
12.15–13.30Lunch, Mathematics lounge, Malott Hall
13.30–14.15 Lionel Levine, Cornell University (Chair: GRG)
Logarithmic fluctuations from circularity
Starting with n particles at the origin in Zd, let each particle in turn perform simple random walk until reaching an unoccupied site. Lawler, Bramson and Griffeath proved that with high probability the resulting random set of n occupied sites is close to a ball. We show that its fluctuations from circularity are, with high probability, at most logarithmic in the radius of the ball, answering a question posed by Lawler in 1995. Our proof uses a type of martingale pioneered by Harry Kesten in his work on DLA. Joint work with David Jerison and Scott Sheffield.
14.15–15.00 Rick Durrett, Duke University
The evolving voter model
In the evolving voter model we choose oriented edges (x,y) at random. If the two individuals have the same opinion, nothing happens. If not, x imitates y with probability 1-α, and otherwise severs the connection with y and picks a new neighbor at random (i) from the graph, or (ii) from those with the same opinion as x. One model has a discontinuous transition, the other a continuous one.
15.15–16.00 Geoffrey Grimmett, Cambridge University (Chair: VS)
Bond percolation on isoradial graphs
Special properties of isoradial embeddings of planar graphs will be discussed in the context of bond percolation. Subject to natural conditions, such models are critical and have certain features of universality. Joint work with Ioan Manolescu.
16.00–16.45 Stanislav Smirnov, Geneva University
Percolation as a noise
Boris Tsirelson conjectured that planar percolation can be thought of as noise, or a continuous product of probability spaces, and pointed out that such noise would have to be “black”, or non-classical. We will discuss our proof with Oded Schramm that percolation is indeed a noise, and its possible consequences.
16.45–17.00 Laurent Saloff-Coste

Closing remarks
17.30–21.00 Dinner