6 papers · 1 filter
Degree corrected stochastic block model: excursion representation
David Clancy, Vitalii Konarovskyi, Vlada Limic
This is the first of two complementary works in which we analyze the connected components of the degree-corrected stochastic block model (DCSBM). Our model is a random graph with a…
A Central Limit Theorem for Modified Massive Arratia Flow
Andrey Dorogovtsev, Vitalii Konarovskyi, Max von Renesse
The modified massive Arratia flow is a model for the dynamics of passive particle clusters moving in a random fluid that accounts for the effects of mass aggregation. We show a cen…
A quantitative central limit theorem for the simple symmetric exclusion process
Benjamin Gess, Vitalii Konarovskyi
A quantitative central limit theorem for the simple symmetric exclusion process (SSEP) on a -dimensional discrete torus is proven. The argument is based on a comparison of the g…
On Number of Particles in Coalescing-Fragmentating Wasserstein Dynamics
Vitalii Konarovskyi
We consider the system of sticky-reflected Brownian particles on the real line proposed in [arXiv:1711.03011]. The model is a modification of the Howitt-Warren flow but now the dif…
On Dean-Kawasaki Dynamics with Smooth Drift Potential
Vitalii Konarovskyi, Tobias Lehmann, Max von Renesse
We consider the Dean-Kawasaki equation with smooth drift interaction potential and show that measure valued solutions exist only in certain parameter regimes in which case they are…
Dean-Kawasaki Dynamics: Ill-posedness vs. Triviality
Tobias Lehmann, Vitalii Konarovskyi, Max-K. von Renesse
We prove that the Dean-Kawasaki SPDE admits a solution only in integer parameter regimes, in which case the solution is given in terms of non-interacting particles.