A Rough Breuer-Major Theorem

A Rough Breuer-Major Theorem
Topic
A Rough Breuer-Major Theorem
Date & Time
Thursday, April 23, 2026 - 16:00 - 17:00
Speaker
Henri Elad Altman, Université Sorbonne Paris Nord
Location
W923, West Hall, NYU Shanghai New Bund Campus

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Abstract:

The celebrated Breuer-Major Theorem (1983) states a CLT for rescaled sums of stationnary sequences of the form f(X_i), where the X_i are Gaussian, not necessarily independent, but with correlations decaying appropriately fast. Functional strenghtenings of this result were later obtained in several articles, one of the sharpest results being derived by Nourdin-Nualart (2020), where an invariance principle is derived under Lp integrability condition on f, for any p>2.
 
I shall present a rough path strengthening of these results showing that, under appropriate differentiability and integrability assumptions on f, the rescaled sums of the variables f(X_i), together with their iterated sums, converge in law to the distribution of a Brownian rough path. This is joint work with Tom Klose (University of Oxford) and Nicolas Perkowski (Freie Universität Berlin).

Biography:

Henri Elad Altman is currently maître de conférence (assistant professor) in Probability at Université Sorbonne Paris Nord. His research focuses on the probabilistic properties of solutions of singular stochastic differential equations, as well as on scaling limits of discrete probabilistic models such as random walks in random environment. He defended his PhD in 2019 under the supervision of Prof. Lorenzo Zambotti at Sorbonne Université in Paris. Between 2019 and 2021 he was Chapman Fellow in Mathematics in the group of Prof. Xue-Mei Li at Imperial College London and, from 2021 to 2023, he worked as a Dirichlet Postdoctoral Fellow in Mathematics in the group of Prof. Nicolas Perkowski at Freie Universität Berlin.

Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai

This event is open to the NYU Shanghai community and Math community.