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math.PR2026
Universal Central Limit Theorem for non-exchangeable interacting diffusions
Mykhaylo Shkolnikov, Lane Chun Yeung
We study non-exchangeable interacting diffusions with pairwise interaction strengths encoded by a sequence of matrices. Under suitable structural and denseness conditions on these…
math.PR2025
Intertwining diffusions and wave equations
Benjamin Budway, Soumik Pal, Mykhaylo Shkolnikov
We develop a general theory of intertwined diffusion processes of any dimension. Our main result gives an SDE construction of intertwinings of diffusion processes and shows that th…
math.PR2024
From rank-based models with common noise to pathwise entropy solutions of SPDEs
Mykhaylo Shkolnikov, Lane Chun Yeung
We study the mean field limit of a rank-based model with common noise, which arises as an extension to models for the market capitalization of firms in stochastic portfolio theory.…