An application of Grothendieck theorem to the theory of multicorrelation sequences, multiple recurrence and partition regularity of quadratic equations

2023/02/24 by Or Shalom, Shalom, Or
Computer Science · Mathematics · #Advanced Topology and Set Theory #Combinatorics #Combinatorics (math.CO) #Computer science #Discrete mathematics #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical and Theoretical Analysis #Mathematics #Measure (data warehouse) #Partition (number theory) #Pure mathematics #Quadratic equation #Space (punctuation) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2302.12857

openalex publication_date 2023/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use Grothendieck theorem to prove a structure theorem for multicorrelation sequences of length two, associated with two (not necessarily commuting) measure preserving actions on a probability space. We use this to deduce a multiple recurrence result concerning products of linear terms, and a partition regularity result of certain systems of quadratic equations, building on the work of Frantzikinakis and Host.

Related

• Uniformity of multiplicative functions and partition regularity of some quadratic equations
• Decomposition of multicorrelation sequences and joint ergodicity
• Decomposition results for multiplicative actions and applications
• Recurrence for stationary group actions
• A view on multiple recurrence