Orthogonal Intertwiners for Infinite Particle Systems in The Continuum

Abstract

This article focuses on a system of sticky Brownian motions, also known as Howitt-Warren martingale problem, and correlated Brownian motions and shows that infinite-dimensional orthogonal polynomials intertwine the dynamics of infinitely many particles and their $n$-particle evolution. The proof is based on two assumptions about the model: information about the reversible measures for the $n$-particle dynamics and consistency. Additionally, explicit formulas for the polynomials are used, including a new explicit formula for infinite-dimensional Meixner polynomials, the orthogonal polynomials with respect to the Pascal process. As an application of the intertwining relations, new reversible measures for the infinite-particle dynamics are obtained.

26 pages

References in corpus (7)

• Duality and hidden symmetries in interacting particle systems
• Reflected planar Brownian motions, intertwining relations and crossing probabilities
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• Sticky-sphere clusters
• KPZ equation limit of sticky Brownian motion
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Cited by in corpus (1)

• Intertwinings for Continuum Particle Systems: an Algebraic Approach