15 citations · 21 across the 9 of their papers we have counts for
9 papers
Finite-dimensional reduction of a Wasserstein gradient flow and sharp decay rates
Dohyun Kim, Hansol Park, Woojoo Shim
We study the Wasserstein gradient flow generated by a family of extended generalized variance functionals, defined as the expected squared -dimensional volume of a simplex, whic…
Higher-order interaction model from geometric measurements
Dohyun Kim, Hansol Park, Woojoo Shim
We introduce a higher simplicial generalization of the linear consensus model which shares several common features. The well-known linear consensus model is a gradient flow with a…
Asymptotic convergence of heterogeneous first-order aggregation models: from the sphere to the unitary group
Dohyun Kim, Hansol Park
We provide the detailed asymptotic behavior for first-order aggregation models of heterogeneous oscillators. Due to the dissimilarity of natural frequencies, one could expect that…
An algebraic approach for the weak coupling of multiple Lohe tensor models
Seung-Yeal Ha, Dohyun Kim, Hansol Park
We present a systematic algebraic approach for the weak coupling of Cauchy problems to multiple Lohe tensor models. For this, we identify an admissible Cauchy problem to the Lohe t…
Collective Dynamics of Lohe type aggregation models
Seung-Yeal Ha, Dohyun Kim
In this paper, we review state-of-the-art results on the collective behaviors for Lohe type first-order aggregation models. Collective behaviors of classical and quantum many-body…
Existence and emergent dynamics of quadratically separable states to the Lohe tensor model
Seung-Yeal Ha, Dohyun Kim, Hansol Park
A tensor is a multi-dimensional array of complex numbers, and the Lohe tensor model is an aggregation model on the space of tensors with the same rank and size. It incorporates pre…