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Orthogonal Stochastic Duality Functions from Lie Algebra Representations.

Wolter Groenevelt1

  • 1Technische Universiteit Delft, DIAM, PO Box 5031, 2600 GA Delft, The Netherlands.

Journal of Statistical Physics
|March 16, 2019
PubMed
Summary
This summary is machine-generated.

Stochastic duality functions for Markov processes are derived using Lie algebra representation theory. This yields orthogonal duality functions expressed via hypergeometric functions for particle and diffusion processes.

Keywords:
Hypergeometric functionsLie algebra representationsOrthogonal polynomialsStochastic duality

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Area of Science:

  • Mathematical Physics
  • Probability Theory
  • Representation Theory

Background:

  • Markov processes are fundamental in modeling random phenomena.
  • Stochastic duality functions offer insights into the behavior of these processes.
  • Representation theory provides powerful tools for analyzing mathematical structures.

Purpose of the Study:

  • To derive stochastic duality functions for specific Markov processes.
  • To explore the connection between representation theory and duality functions.
  • To identify applications in interacting particle and diffusion systems.

Main Methods:

  • Utilized representation theory of Lie algebras.
  • Employed unitary intertwiners between representations.
  • Investigated representations of the Heisenberg algebra and .

Main Results:

  • Obtained stochastic duality functions from the kernel of unitary intertwiners.
  • Established generalized orthogonality relations for these duality functions.
  • Derived orthogonal (self-)duality functions in terms of hypergeometric functions.

Conclusions:

  • The study successfully links Lie algebra representation theory to stochastic duality.
  • The derived functions provide a novel framework for analyzing specific interacting particle and diffusion processes.
  • The results highlight the utility of hypergeometric functions in this context.