Sunday 20 November 2011
Malott Hall 406, Cornell University
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 |
| Welcome | |
| 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. | |
| 12.15–13.30 | Lunch, 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. | |
| 15.00–15.15 | Break |
| 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 |