Vitalii Konarovskyi is a mathematician working in probability theory working on stochastic analysis and interacting particle systems. In his paper on coalescing heavy diffusion particles, he constructed a modified Arratia flow in which particles carry conserved mass and their diffusion rate is inversely proportional to that mass, starting from uniformly distributed mass on an interval.[ref]
The mechanism is easy to picture: after particles merge, the heavier cluster diffuses more slowly. A rigorous construction must accommodate a continuum of initial particles, rather than only a finite collection of independent paths. His work develops a stochastic integral for the resulting flow and describes total local time through an occupation measure. His authored notes on the large deviation principle also explain how unlikely fluctuations acquire quantitative path costs.[ref]
Figure 1.
Vitalii Konarovskyi at Oberwolfach, from his author homepage
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