Statistics and Probability Seminar Series

See also our calendar for a complete list of the Department of Mathematics and Statistics seminars and events.

Please email Guangqu ZHENG (gzheng90@bu.edu) if you would like to be added to the email list.

Fall 2026 Dates

(Time/location: Thursdays 4-5pm/CDS 365)

September 10: Youssef Hakiki (Purdue)

Title: On Itô-Stratonovich formula for rough sheets
Abstract: We explore a new strategy towards an Itô-Stratonovich type formula for rough sheets. Historically, planar integration for irregular paths has been notoriously cumbersome. The emergence of ”mixed differential” terms in 2D leads to overlapping iterated integrals, which previously required the construction of exhaustive combinatorial structures. As an example of this kind of structure, let us mention the massive 36-element planar signature introduced by K. Chouk and M. Gubinelli (Rough sheets. https://arxiv.org/pdf/1406.7748, 2014). In this work we propose a simplified setting for rough calculus in the plane, which relies on elementary Taylor expansions in a more fundamental way. We claim that this simple trick allows us to significantly streamline the complexity of planar algebraic integration. We illustrate this methodology for a specialized Rough-Young framework: we extend the classical planar change-of-variable formula to paths possessing an asymmetric Hölder regularity: \gamma_1 > 1/3 in the first direction and \gamma_2 > 1/2 in the second direction. Relying on a structured controlled path expansions, we rigorously minimize the set of iterated integrals needed in the signature, and express the resulting planar change-of-variable formula as the explicit limit of Riemann sums.

September 17: Richard Sowers (UIUC)

Title: Side boundary conditions for a Kolmogorov Diffusion
Abstract: We consider a Kolmogorov-type PDE corresponding to a particle under white noise force. We are interested in stopping the process at a fixed position, i.e., imposing Dirichlet conditions at a side boundary. We construct a simple Gaussian heat kernel inside the domain, and investigate a boundary-layer kernel, connected to some work by McKean. We show that this boundary layer heat kernel has a novel jump condition. We outline a polynomial expansion of for the heat kernels, and then construct a Volterra equation for solving the original problem. The novel jump leads to a periodic structure of the Volterra equation.

September 24: no talk, faculty meeting

October 1: Firas Rassoul-Agha (University of Utah)

Title: Shocks, instability, and the twenty networks of infinite geodesics in the Directed Landscape
Abstract: For stochastic Hamilton-Jacobi equations, instability points are where two eternal solutions with the same asymptotic velocity differ, while shocks are where the velocity field is discontinuous. We analyze these structures for the KPZ fixed point, the central object of the KPZ universality class. We describe the geometry of the instability region, show that it can be determined by the shock structures of the two eternal solutions, and obtain a complete classification of semi-infinite geodesics/characteristics. We also identify the Martin boundary and its minimal part with horofunctions and Busemann functions, respectively. As a consequence of instability, the Martin boundary is strictly larger than its minimal part. This is joint work with Mikhail Sweeney.

October 2 (Friday; unusual): Xiao Shen (North Carolina State University)

Title: Negative association of Busemann functions in exponential last-passage percolation
Abstract: One hallmark of exactly solvable KPZ random growth models is product-form invariant measures. In the setting of exponential last-passage percolation (LPP), this corresponds to the independence of Busemann increments along any down-right path. However, this independence breaks down when multiple asymptotic directions are considered simultaneously, owing to the fact that jointly invariant measures are not jointly product-form. This paper shows that the failure of independence is one-sided: Busemann increments across arbitrary directions are negatively associated. As an application, we derive an exponential concentration inequality for sums of Busemann increments on the diffusive scale, even when the increments are not independent. While our argument relies on a Burke property that is special to exponential weights, all other proof ingredients—including hidden LPP monotonicities and braid relations for queueing maps—hold for arbitrary weights. (Joint work with Erik Bates.)

October 8: Zhengjiang Lin (MIT)

Title: Mean-Field Transformer Dynamics: Long-Time Behavior and Propagation of Chaos
Abstract: Transformers process information through repeated self-attention layers. In a continuous-depth model, token representations evolve as interacting particles, and their mean-field dynamics are governed by a nonlinear and nonlocal transport equation. This perspective raises two mathematical questions: how do token distributions evolve as the number of layers grows, and how accurately does a finite context approximate its population limit? In this talk, I will present results addressing both questions. I will first discuss the long-time behavior of mean-field attention dynamics. For attractive interactions, we prove exponential synchronization under suitable assumptions, quantifying the collapse of token representations associated with oversmoothing. For repulsive interactions, we establish convergence to the uniform measure through an entropy dissipation argument, despite the absence of geodesic convexity of the interaction energy in Wasserstein space. This argument extends to a broader class of interaction kernels and yields sharp bounds on energy decay. I will then turn to finite-context approximation. The contextual flow formulation provides an idealized model of in-context learning, where the context consists of demonstrations sampled from a task distribution. Propagation of chaos quantifies how the output based on finitely many demonstrations approximates its population-context limit. Combining these estimates with an Eulerian adjoint formulation of the loss gradient, we obtain optimal rates of order $n^{-1/2}$, where $n$ is the context length, for transformer-based contextual flows in both inference and training. Under sufficiently strong regularization, the training estimates remain uniform over online gradient descent iterations. This talk is based on joint work with Shi Chen, Kaizhao Liu, Yury Polyanskiy, and Philippe Rigollet.

October 15: Roger Van Peski (Columbia University)

Title: New results for dimers with quenched disorder
Abstract: The dimer model, i.e. random perfect matchings of a bipartite graph, is a classical object about which much is known. As soon as one biases the probability measure by edge weights which are themselves random, very little is known rigorously, though physicists have studied such models for several decades and made extensive predictions. I will discuss a new integrable model in this class (the Gamma-disordered Aztec diamond) which allows us to prove results on the free energy, and also exhibits surprising relations to integrable polymer models which lead to probabilistic results on tilings. Joint work with Maurice Duits (KTH), https://arxiv.org/abs/2512.03033.

October 22: Yang Feng (NYU)

Title: Adaptive Knowledge Transfer: Statistical Foundations, Representation Learning, and Federated AI
Abstract: Leveraging knowledge across related tasks or domains through transfer and multi-task learning is essential for building sample-efficient models, especially when labeled data in the target domain is scarce or expensive. Four challenges stand in the way: the similarity between sources and the target is unknown, some sources may be contaminated or adversarially corrupted, the data are often high dimensional, and raw data frequently cannot leave the site that collected it. This talk presents a unified statistical perspective on adaptive knowledge transfer that addresses these challenges across four learning paradigms. We begin with high-dimensional generalized linear models, where a transferable-source detection step followed by pretraining and fine-tuning adapts automatically to the unknown similarity and is never worse than learning from the target alone. We then turn to representation multi-task learning, in which tasks share an approximately common low-dimensional representation and a fraction of tasks may be arbitrarily contaminated; we establish the minimax rate, interpret its terms through the pretraining and fine-tuning pipeline, and give adaptive and robust algorithms that attain it. Third, we consider unsupervised federated learning for mixture models, where a federated gradient EM algorithm with a robust aggregation step achieves non-asymptotic guarantees, and we show how to align cluster labels across sites and handle sites whose cluster sets differ. Finally, we study federated transfer learning under differential privacy, introducing a federated privacy model that sits between the central and local models, characterizing its minimax rates, and showing that private source detection achieves them adaptively. Throughout, minimax theory reveals the price of heterogeneity, contamination, dimension, and privacy, and in doing so provides principled guidance for designing robust and scalable AI systems.