The Fourteenth Northeast Probability Seminar (NEPS) will be held at NYU’s Kimmel Center (Room 912/914) on November 19th and Room 109 of the Courant Institute, NYU, on November 20th, 2015.

**Details**

The invited speakers are:

- Jian Ding (University of Chicago)

“Some geometric aspects for two-dimensional Gaussian free fields.” - Francis Comets (Université Paris Diderot)

“Localization in one-dimensional log-gamma polymers” - Jean-François Le Gall (University Paris-Sud Orsay)

“First-passage percolation on random planar graphs.” - Mykhaylo Shkolnikov (Princeton University)

“Edge of beta ensembles and the stochastic Airy semigroup.”

**Please note:**

- Financial support is still available.

**Financial support to attend the conference.**The NSF grant allows us to offer some financial support to

participants from US Universities. We will give preference to graduate

students, postdocs, women and minorities, and junior faculty.Applicants for this financial support should provide:- a one-page letter explaining their interest in the seminar and its relation to their research interests
- a current CV
- graduate students and postdocs should also arrange for a letter of recommendation to be sent from their advisor or some expert familiar with their work

Materials should be sent either by e-mail (preferred) or postal mail to:

Ivan Matic

Department of Mathematics, 6th Floor, Room 6-230

Baruch College of the City University of New York

One Bernard Baruch Way (55 Lexington Ave. at 24th St)

New York, NY 10010

ivan.matic@baruch.cuny.edu - There will be a dinner for women in probability:

*Women in Probability*is an organization for women active in probability research. Our primary purpose is to provide networking and mentoring opportunities for early career women. Our activities are funded by the NSF. For more information on Women in Probability and its activities, please visit our website womeninprobability.org.

Abstracts:

**Jian Ding (University of Chicago)**

“Some geometric aspects for two-dimensional Gaussian free fields”:I will give a review on recent progresses on extreme values of two-dimensional discrete Gaussian free field, including the law of convergence for the centered maximum as well as the universality (for the maximum) among log-correlated Gaussian fields. Then, I will discuss the first passage percolation where the vertex weight is given by exponentiating the field, and present some recent result on the universality (non-universality) on such FPP metric in the class of log-correlated Gaussian field.Based on joint works with Maury Bramson, Subhajit Goswami, Rishideep Roy, Ofer Zeitouni and Fuxi Zhang in various combinations.**Francis Comets (Université Paris Diderot)**

“Localization in one-dimensional log-gamma polymers”:Directed polymers in random environment are known to localize when the disorder is strong. We can analyse this in a precise manner for the directed polymer in one space dimension in log-gamma environment with boundary conditions, introduced by Sepp{\”a}l{\”a}inen. In the equilibrium case, we prove that the end point of the polymer converges in law as the length increases, to a density proportional to the exponent of a zero-mean random walk. This holds without space normalization, and the mass concentrates in a neighborhood of the minimum of this random walk. Joint work with V.-L. Nguyen.**Jean-François Le Gall (University Paris-Sud Orsay)**

“First-passage percolation on random planar graphs”We study local modifications of the graph distance in large random triangulations. Our main results show that, in large scales, the modified distance behaves like a deterministic constant c times the usual graph distance. This applies to the first-passage percolation distance obtained by assigning independent random weights to the edges of the graph. We also consider distances on the dual map, and in particular the first-passage percolation with exponential edge weights, which is closely related to the so-called Eden model. In the latter case, we are able to compute explicitly the constant c. In general however, the constant c is obtained from a subadditivity argument in the infinite half-plane model that describes the asymptotic shape of the triangulation near the boundary of a large ball. Our results apply in particular to the infinite random triangulation known as the UIPT, and show that balls of the UIPT for the first-passage percolation distance are asymptotically close to balls for the graph distance. This is a joint work with Nicolas Curien.**Mykhaylo Shkolnikov (Princeton University)**

“Edge of beta ensembles and the stochastic Airy semigroup”Beta ensembles arise naturally in random matrix theory as a

family of point processes, indexed by a parameter beta, which

interpolates between the eigenvalue processes of the Gaussian

orthogonal, unitary and symplectic ensembles (GOE, GUE and GSE). It is

known that, under appropriate scaling, the locations of the rightmost

points in a beta ensemble converge to the so-called Airy(beta)

process. However, very little information is available on the

Airy(beta) process except when beta=2 (the GUE case). I will explain

how one can write a distribution-determining family of observables for

the Airy(beta) process in terms of a Brownian excursion and a Brownian

motion. Along the way, I will introduce the semigroup generated by the

stochastic Airy operator of Ramirez, Rider and Virag. Based on joint

work with Vadim Gorin.