The seminar is organized by the Mathematics and Statistics departments and covers topics in pure and applied probability.

Organizers: Guillaume Barraquand, Ivan Corwin, Julien Dubedat, Ioannis Karatzas, Jeffrey Kuan, Marcel Nutz, Philip Protter, Hao Shen, Yi Sun, and Li-Cheng Tsai.

Meeting Time: Wednesday 5:30-6:30 pm and Friday 12:00-1:00 pm

Location: Math 520 (Directions to the Mathematics Department)

Click here to join the mailing list.

Contact: probability_seminar@math.columbia.edu

Date and Time | Speaker | Title |
---|---|---|

Friday, February 3 12-1 pm |
Allan Sly (Princeton) | First passage percolation on rotationally invariant fieldsI will discuss new results on continuum models of first passage percolation which are rotationally invariant. For such models we give a multi-scale argument showing that the variance grows as O(n^{1-\epsilon}). Joint work with Riddhipratim Basu and Vladas Sidoravicius |

Friday, February 10 12-1 pm |
Firas Rassoul-Agha (Utah) | KPZ wandering exponent for random walk in i.i.d. dynamic Beta random environmentWe condition random walk in an i.i.d. dynamic Beta random environment to escape at an atypical velocity. The conditioned process converges to another random walk in random environment (RWRE). The new environment is a Doob transform of the original one by a harmonic function that is a Busemann type limit and solves a variational formula for the quenched large deviation rate function. Along the way we construct the stationary Beta polymer and prove fluctuation bounds for it. The Doob conditioned RWRE is in duality with this polymer and as a result it has a KPZ wandering exponent of 2/3. |

Wednesday, February 15 5:30-6:30 pm |
Praveen Kolli (CMU) | Fluctuations of diffusions interacting through the ranksWe study the fluctuations of a system of diffusions interacting through the ranks when the number of diffusions goes to infinity. It is known that the empirical cumulative distribution function of such diffusions converges to a non-random limiting cumulative distribution function which satisfies the porous medium PDE. We show that the fluctuations of the empirical cumulative distribution function around its limit are governed by a suitable SPDE. (Joint work with Misha Shkolnikov) |

Friday, February 17 9am-1pm 413 Kent |
Columbia University Symposium on Probability & Society | |

Wednesday, February 22 5:30-6:30 pm |
Tobias Johnson (NYU) | Galton-Watson fixed points, tree automata, and interpretationsConsider a set of trees such that a tree belongs to the set if and only if at least two of its root child subtrees do. One example is the set of trees that contain an infinite binary tree starting at the root. Another example is the empty set. Are there any other sets satisfying this property other than trivial modifications of these? I'll demonstrate that the answer is no, in the sense that any other such set of trees differs from one of these by a negligible set under a Galton-Watson measure on trees, resolving an open question of Joel Spencer's. This follows from a theorem that allows us to answer questions of this sort in general. All of this is part of a bigger project to understand the logic of Galton-Watson trees, which I'll tell you more about. Joint work with Moumanti Podder and Fiona Skerman. |

Friday, March 3 12-1 pm |
Boris Hanin (MIT) | Airy scaling of random Hermite functions at the causticRandom Hermite functions are eigenfunctions of fixed energy for the isotropic harmonic oscillator in R^d. They therefore transition from highly oscillatory to exponentially damped at the caustic, the analog of the edge of the spectrum in random matrix theory. The purpose of this talk is to explain how the Airy kernel and its relatives appear in the scaling limit of random Hermite functions around the caustic as Planck's constant h goes to 0. Rather than being the kernel of the determinantal process, the Airy kernel will appear as the covariance function of a limit Gaussian field. This is joint work with Steve Zelditch and Peng Zhou. |

Wednesday, March 8 5:30-6:30 pm |
Lisa Hartung (NYU) | TBA |

Friday, March 24 12-1 pm |
Haya Kaspi (Technion) | TBA |

Friday, March 31 | Columbia-Princeton Probability Day | |

Wednesday, April 19 4:30-7:15 pm |
Columbia-Courant Probability Seminar Jean Bertoin (Zurich) 4:30-5:30 pm (colloquium) Zhou Fan (Stanford) 5:45-6:30 pm Cyril Labbé (Paris-Dauphine) 6:30-7:15 pm |
TBA |

Friday, April 21 | Applied Probability Day |