The CUNY Probability Seminar is typically held on Tuesdays from 4:15 to 5:15 pm at the CUNY Graduate Center Math Department. The exact dates, times and locations are mentioned below. If you want to talk at the seminar, or want to be added to/removed from the seminar mailing list, then please contact the Seminar Coordinator

*Jack Hanson *(http://jhanson.ccny.cuny.edu/)

**Tuesday, February 6, 2018, 4:15 PM, Rm. 3307:**

**Speaker: **Joshua Rosenberg, UPenn

**Title**: Invasion Percolation on Galton-Watson Trees

**Abstract**: This talk will focus on invasion percolation on Galton-Watson trees. On almost every Galton-Watson tree, the invasion cluster almost surely contains only one infinite path. This means that for almost every Galton-Watson tree, invasion percolation induces a probability measure on infinite paths from the root. I will discuss our proof demonstrating that under certain conditions of the progeny distribution, this measure is absolutely continuous with respect to the limit uniform measure. This confirms that invasion percolation, an efficient self-tuning algorithm, may be used to sample approximately from the limit uniform distribution. Time permitting, I will also discuss a related result we achieved which involved proving a limit law for the forward maximal weights along the backbone of the invasion cluster. This is based on joint work with Marcus Michelen and Robin Pemantle.

**Tuesday, February 13, 4:15 PM, Rm. 3307:**

**Speaker: ** Jay Rosen, CUNY (College of Staten Island)

**Title: **Tightness for the Cover Time of compact two dimensional manifolds

**Abstract: **Let $\CC^\ast_{\ep,M}$ denote the cover

time of the two dimensional compact manifold $M$ by

a Wiener sausage of radius $\ep$. We prove that

$$\sqrt{\CC^{\ast}_{\ep,M} }

-\sqrt{\frac{2A_{M}}{\pi}}\(\log \ep^{-1}-\frac14\log\log \ep^{-1}\)$$ is tight, where $A_{M}$ denotes the Riemannian area of $M$.

Joint work with David Belius and Ofer Zeitouni

**Tuesday, February 27, 4:15 PM, Rm. 3307:**

**Speaker: **Shirshendu Chatterjee, CUNY (City College)

**Title: **TBA

**Abstract:TBA
**

**Tuesday, March 6, 4:15 PM, Rm. 3307:**

**Speaker: **Yuri Bakhtin, NYU

**Title: **Invariant densities for systems with random switchings

**Abstract: **In piecewise deterministic Markov processes, the system solves an ODE with the right-hand side that switches randomly between vector fields from a fixed family. I will talk about smoothness and singularities of invariant distributions for such systems. The most recent progress is inspired by the Malliavin calculus approach to hypoellipticity in diffusion processes. Joint work with Tobias Hurth, Jonathan Mattingly, Sean Lawley.

**Tuesday, March 20, 4:15 PM, Rm. 3307:**

**Speaker: **Alexander Moll, HCM

**Title: **Random Permutations and the Quantum Linear Wave Equation

**Abstract: **The quantum linear wave equation – also known as the free massless scalar bosonic quantum field – is a geometric quantization Q with respect to the Peierls bracket of the classical linear wave equation for u(x,t) for x on any Riemannian manifold (X,g). We first define from probabilistic first principles (without using path integrals) the Fock space of a Sobolev space, the quantization Q, phonon number states, mixed thermal states, and pure coherent states. Next, we describe the distributions of observables in coherent states as fractional Gaussian fields and describe the h^{1/2} correction in the semi-classical limit at fixed time by specializing a general result from [A. Moll 2017]. Finally, we specialize to the quantum linear wave equation in (1+1) dimensions, where we encounter simultaneously two objects of recent interest in extreme value theory:

(I) the number of k-cycles in a random permutation of size d with law weighted by arbitrary multiplicative cycle weights possibly depending on d

(II) regularized exponentials of log-correlated fractional Gaussian fields in 1D

and relate their asymptotics to the semi-classical analysis of coherent states.

**Tuesday, March 27, 4:15 PM, Rm. 3307:**

**Speaker: **Li-Cheng Tsai, Columbia

**Title: **KPZ equation limit for the six vertex model

**Abstract: **The Six Vertex (6V) model, initially introduced as a model for ice, is an integrable model for tiling in two dimensions. In this talk we consider symmetric and stochastic 6V models, and show that, under certain scaling into the ferroelectric/disordered phase critical point, fluctuations described by the Kardar–Parisi–Zhang (KPZ) equation arises.

**Tuesday, April 10, 4:15 PM, Rm. 3307:**

**Speaker: **Arjun Krishnan, U. of Rochester

**Title: **TBA

**Abstract: **TBA

**Tuesday, April 17, 4:15 PM, Rm. 3307:**

**Speaker: **Philippe Sosoe, Cornell University

**Title: **Dispersive equations with random initial data

**Abstract: **Beginning the 1980s, there has been interest in considering certain classical nonlinear equations such as nonlinear Schroedinger, Korteweg de Vries and wave equations, with random initial data. I will explain the motivation for this setting, describe some of the results obtained by using probabilistic methods for dispersive nonlinear equations, and finish by describing some recent and ongoing work by myself and collaborators on the subject.

**Tuesday April 24, 4:15 PM, Rm. 3307**

**Speaker: **Guillaume Dubach

**Title: **Eigenvectors of non-hermitian random matrices

**Abstract: **Eigenvectors of non-hermitian matrices are non-orthogonal, and their distance to a unitary basis can be quantified through the matrix of overlaps. These variables quantify the stability of the spectrum, and characterize the joint eigenvalues increments under Dyson-type dynamics. They first appeared in the physics literature; well known work by Chalker and Mehlig calculated the expectation of these overlaps for complex Ginibre matrices. For the same model, we extend their results by deriving the distribution of the overlaps and their correlations. (Joint work with P. Bourgade)

**Tuesday May 1, 4:15 PM, Rm. 3307**

**Speaker: **Matthew Junge, Duke U.

**Title: **TBA

**Abstract: **TBA

**Tuesday May 8, 4:15 PM, Rm. 3307**

**Speaker: **Murad Taqqu, Boston University

**Title:** Levy driven Ornstein-Uhlenbeck type processes and intermittency

**Abstract: **We consider finite variance Levy driven Ornstein-Uhlenbeck processes. Although these processes provide a rich class of stationary models, their dependence structure is rather limited from a modeling perspective. But superpositions of such Ornstein-Uhlenbeck processes introduced by Barndorff-Nielsen, provide far more flexibility and can exhibit both short-range dependence and long-range dependence. They have found many applications, especially in finance where they are used in models for stochastic volatility. The asymptotic behavior of such processes, integrated and normalized, can be, however, unusual. The cumulants and moments turn out to have an unexpected rate of growth, akin to a physical phenomenon called intermittency. Self-similarity of the limit and intermittency, however, are typically not compatible. We will try to shed some light on this unusual situation.

**Tuesday May 15, 4:15 PM, Rm. 3307**

**Speaker: **Sixian Jin, Fordham U.

**Title: **TBA

**Abstract: **TBA