45 citations · 120 across the 16 of their papers we have counts for
17 papers
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…
Stochastic Modified Flows, Mean-Field Limits and Dynamics of Stochastic Gradient Descent
Benjamin Gess, Sebastian Kassing, Vitalii Konarovskyi
We propose new limiting dynamics for stochastic gradient descent in the small learning rate regime called stochastic modified flows. These SDEs are driven by a cylindrical Brownian…
Conservative SPDEs as fluctuating mean field limits of stochastic gradient descent
Benjamin Gess, Rishabh S. Gvalani, Vitalii Konarovskyi
The convergence of stochastic interacting particle systems in the mean-field limit to solutions of conservative stochastic partial differential equations is established, with optim…
On Moments of Multiplicative Coalescents
Vitalii Konarovskyi, Vlada Limic
We prove existence of all moments of the multiplicative coalescent at all times. We obtain as byproducts a number of related results which could be of general interest. In particul…
Spectral gap estimates for Brownian motion on domains with sticky-reflecting boundary diffusion
Vitalii Konarovskyi, Victor Marx, Max von Renesse
Introducing an interpolation method we derive lower bounds for the spectral gap for Brownian motion on general domains with sticky-reflecting boundary diffusion associated to the f…
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 Conditioning Brownian Particles to Coalesce
Vitalii Konarovskyi, Victor Marx
We introduce the notion of a conditional distribution to a zero-probability event in a given direction of approximation, and prove that the conditional distribution of a family of…
Stochastic Block Model in a new critical regime and the Interacting Multiplicative Coalescent
Vitalii Konarovskyi, Vlada Limic
This work exhibits a novel phase transition for the classical stochastic block model (SBM). In addition we study the SBM in the corresponding near-critical regime, and find the sca…
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.
Coalescing-fragmentating Wasserstein dynamics: particle approach
Vitalii Konarovskyi
We construct a family of semimartingales that describes the behavior of a particle system with sticky-reflecting interaction. The model is a physical improvement of the Howitt-Warr…
Reversible Coalescing-Fragmentating Wasserstein Dynamics on the Real Line
Vitalii Konarovskyi, Max von Renesse
We introduce a family of reversible fragmentating-coagulating processes of particles of varying size-scaled diffusivity with strictly local interaction on the real line as mathemat…
On asymptotic behavior of the modified Arratia flow
Vitalii Konarovskyi
We study asymptotic properties of the system of interacting diffusion particles on the real line which transfer a mass [arXiv:1408.0628]. The system is a natural generalization of…
Modified Massive Arratia flow and Wasserstein diffusion
Vitalii Konarovskyi, Max von Renesse
Extending previous work [arXiv:1408.0628] by the first author we present a variant of the Arratia flow, which consists of a collection of coalescing Brownian motions starting from…
A system of coalescing heavy diffusion particles on the real line
Vitalii Konarovskyi
We construct a modified Arratia flow with mass and energy conservation. We suppose that particles have a mass obeying the conservation law, and their diffusion is inversely proport…