29 citations · 108 across the 9 of their papers we have counts for
12 papers
Fréchet Barycenters and a Law of Large Numbers for Measures on the Real Line
Alexey Kroshnin, Andrei Sobolevski
Endow the space of probability measures on with a transportation cost generated by a translation-invariant convex cost function. Fo…
Droplet condensation and isoperimetric towers
Matteo Novaga, Andrei Sobolevski, Eugene Stepanov
We consider a variational problem in a planar convex domain, motivated by statistical mechanics of crystal growth in a saturated solution. The minimizers are constructed explicitly…
On dynamics of Lagrangian trajectories for Hamilton-Jacobi equations
Konstantin Khanin, Andrei Sobolevski
Characteristic curves of a Hamilton-Jacobi equation can be seen as action minimizing trajectories of fluid particles. However this description is valid only for smooth solutions. F…
Universal algorithms for solving the matrix Bellman equations over semirings
Grigory L. Litvinov, Anatoly Ya. Rodionov, Sergei N. Sergeev +1
This paper is a survey on universal algorithms for solving the matrix Bellman equations over semirings and especially tropical and idempotent semirings. However, original algorithm…
Minimum-weight perfect matching for non-intrinsic distances on the line
Julie Delon, Julien Salomon, Andrei Sobolevski
Consider a real line equipped with a (not necessarily intrinsic) distance. We deal with the minimum-weight perfect matching problem for a complete graph whose points are located on…
Local matching indicators for transport problems with concave costs
Julie Delon, Julien Salomon, Andrei Sobolevskii
In this paper, we introduce a class of indicators that enable to compute efficiently optimal transport plans associated to arbitrary distributions of N demands and M supplies in R…