Higher order fluctuation fields and orthogonal duality polynomials
Mario Ayala, Gioia Carinci, Frank Redig
Abstract
<p>Inspired by the works in [2] and [11] we introduce what we call k-th-order fluctuation fields and study their scaling limits. This construction is done in the context of particle systems with the property of orthogonal self-duality. This type of duality provides us with a setting in which we are able to interpret these fields as some type of discrete analogue of powers of the well-known density fluctuation field. We show that the weak limit of the k-th order field satisfies a recursive martingale problem that corresponds to the SPDE associated with the kth-power of a generalized Ornstein-Uhlenbeck process.</p>
Topics & Concepts
MathematicsDuality (order theory)Martingale (probability theory)Scaling limitOrthogonal polynomialsType (biology)Limit (mathematics)Pure mathematicsScalingProperty (philosophy)Order (exchange)Ordered fieldContext (archaeology)Discrete mathematicsMathematical analysisApplied mathematicsFinanceBiologyPhilosophyEpistemologyGeometryPaleontologyEconomicsEcologyTheoretical and Computational PhysicsStochastic processes and statistical mechanicsRandom Matrices and Applications