# Amir Dembo to deliver Hotelling Lectures

**April 18, 2023**

The Hotelling Lectures are an annual event in the Department of Statistics & Operations Research at the University of North Carolina – Chapel Hill, honoring the memory of Professor Harold Hotelling our first chairman. This year we are honored to have Professor Amir Dembo from Stanford University to deliver our two Hotelling lectures which are open to the public.

**Biography**

Amir Dembo obtained his PhD in Electrical Engineering from Technion, Israel. Since 1990, he has been on the faculty of Stanford University and since 2012 as the Marjorie Mhoon Fair Professor in Quantitative Science. His areas of specialization are probability theory and stochastic processes, information theory, large deviations, and their applications in in communication, control, and biomolecular sequence analysis. Together with Ofer Zeitouni, he has authored a book on the theory of large deviations which is now a classical reference in the field. He has served as editor of Probability Theory and Related Fields and of the Annals of Probability. He is a fellow of the Institute of Mathematical Statistics, and in 2022 was elected to the National Academy of Sciences.

**Non-linear Large Deviations and Applications**

*Monday, April 24, 2023 (3:30-4:30pm 209 Manning Hall)*

*Reception following the lecture 4:30-5:30pm in the 3rd Floor lounge of Hanes Hall*

I will overview the emerging theory of nonlinear large deviations, in particular for establishing the naive mean field approximation for certain Gibbs measures and its relation to the representation of such measures as mixtures of not too many product measures. Among the applications we explore, are the abundance of certain patterns in sparse random graphs, having many arithmetic progressions in a random set, and the universality of the Potts model on graphs of growing average degrees.

**Sparse Random Graphs with Unusually Large Subgraph Counts**

*Wednesday, April 26, 2023 (3:30-4:30pm 120 Hanes Hall)*

*Reception prior to the lecture 3:00-3:30pm in the 3rd Floor lounge of Hanes Hall*

In this talk, based on joint works with Nicholas Cook, Huy Tuan Pham and Sohom Bhattacharya, I will discuss recent developments in the study of the upper tails for counts of several fixed subgraphs in a large sparse random graph (such as Erdős–Rényi or uniformly d-regular). These results allow in turn to determine the typical structure of samples from an associated class of Gibbs measures, known as Exponential Random Graph Models, which are widely used in the analysis of social networks.