Homomorphisms relative to additive convolutions and max-convolutions: free, boolean and classical cases
Takahiro Hasebe, Yuki Ueda
TL;DR
This paper introduces new homomorphisms related to additive and max-convolutions across free, boolean, and classical probability theories, emphasizing the significance of limit distributions in free multiplicative laws.
Contribution
It presents novel homomorphisms for various convolutions and highlights their connection to limit distributions in free probability.
Findings
New homomorphisms for additive and max-convolutions introduced
Limit distributions are crucial in free multiplicative laws
Bridges between free, boolean, and classical probability established
Abstract
We introduce new homomorphisms relative to additive convolutions and max-convolutions in free, boolean and classical cases. Crucial roles are played by the limit distributions for free multiplicative law of large numbers.
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Taxonomy
TopicsRandom Matrices and Applications · Stochastic processes and statistical mechanics · Advanced Algebra and Geometry