38 citations · 150 across the 39 of their papers we have counts for
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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…
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.…
Multilevel Dyson Brownian motions via the superposition principle
Benjamin Budway, Mykhaylo Shkolnikov
Multilevel Dyson Brownian motions (MDBMs) combine Dyson Brownian motions of different dimensions into a single process in a canonical way. This paper completes the theory of MDBMs…
Well-posedness of the supercooled Stefan problem with oscillatory initial conditions
Scander Mustapha, Mykhaylo Shkolnikov
We study the one-phase one-dimensional supercooled Stefan problem with oscillatory initial conditions. In this context, the global existence of so-called physical solutions has bee…
Stefan problem with surface tension: global existence of physical solutions under radial symmetry
Sergey Nadtochiy, Mykhaylo Shkolnikov
We consider the Stefan problem with surface tension, also known as the Stefan-Gibbs-Thomson problem, in an ambient space of arbitrary dimension. Assuming the radial symmetry of the…
A singular two-phase Stefan problem and particles interacting through their hitting times
Graeme Baker, Mykhaylo Shkolnikov
We consider a probabilistic formulation of a singular two-phase Stefan problem in one space dimension, which amounts to a coupled system of two McKean-Vlasov stochastic differentia…