## Tuesdays 4.30-5.30 pm,
MR 12.
Webpage of the probability group Tea beforehand at 4pm in the common room, and drinks afterwards at the Punter. |

Date | Speaker | Title | Notes |

12 October | Ronnie Sircar (Princeton) | Stochastic Differential Games and Applications to Energy and Consumer Goods Markets (abstract) | |

19 October | Christophe Garban (CNRS, Lyon) | Near-critical scaling limits (abstract) | |

26 October | Bernard Derrida (ENS Paris) | Statistics at the tip of a branching random walk, and simple models of evolution with selection (abstract) | |

2 November | Arnab Sen (Cambridge) | Coalescing systems of non-Brownian particles (abstract). | |

4 November | Fabrice Debbasch (Paris VI) | Relativistic stochastic processes (abstract). | Note special day and time: 4pm |

9 November | Stephanie Jacquot (Cambridge) | Bulk scaling limit of the Laguerre ensemble (abstract). | |

16 November | No seminar that day. | ||

23 November | Ismael Bailleul (Cambridge) | Lifetime of relativistic diffusions (abstract). | |

26 November | Stephane Boucheron (Paris VII) | Concentration inequalities by the entropy method, variations (details) | Joint with statistics |

30 November | Michael Keane (Wesleyan University) | TBA (abstract) | Talk at 2 pm. |

Consider percolation on the triangular grid in the plane. The scaling limit (as n goes to infinity) of a critical rescaled percolation \omega_{p_c}^n on the triangular grid of mesh 1/n is a very rich probabilistic object (it is the analog of the Brownian motion for the Random walk), and is now well understood thanks to the works of Smirnov and Schramm.

The purpose of a joint work with Gabor Pete and Oded Schramm is to ``visualize'' the phase transition which occurs at p_c, from the perspective of the scaling limit. A first natural attempt in this direction is to consider the scaling limit as n goes to infinity of non-critical rescaled percolations \omega_p^n (with p \neq p_c). Unfortunately, such scaling limits are "degenerate". In order to obtain non-trivial "off-critical" scaling limits, $p$ and $n$ need to be rescaled accordingly.

I will describe in this talk what the natural renormalization is if one wishes to observe the emergence of an infinite cluster, seen from the continuous. The main result in joint work with G. Pete and O. Schramm is that "up to scaling", there is a unique near-critical scaling limit. This near-critical limit is not conformally invariant anymore, but one can nevertheless give a precise description of its "conformal defect".

Finally, I will discuss some new results about dynamical and near-critical regimes in the case of dependent models like the Ising model or the Random-Cluster model.

We shall investigate in this talk one aspect of this geometry/probability correspondence. Dating back to Penrose and Hawking's results, it is now well-established that the appearance of singularities in Einstein's theory of gravitation is unavoidable under quite natural assumptions. Although there is no definitive agreement on what should be called a singularity of spacetime, a largely used notion of singularity is the existence in spacetime of incomplete geodesics. Is there a link between geodesic and probabilistic incompleteness? This will be the main question will shall adress.