38 citations · 150 across the 39 of their papers we have counts for
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math.PR2010★ 14 cited
Concentration of measure for systems of Brownian particles interacting through their ranks
Soumik Pal, Mykhaylo Shkolnikov
We consider a finite or countable collection of one-dimensional Brownian particles whose dynamics at any point in time is determined by their rank in the entire particle system. Us…
math.PR2010★ 2 cited
Large systems of diffusions interacting through their ranks
Mykhaylo Shkolnikov
We study the limiting behaviour of the empirical measure of a system of diffusions interacting through their ranks when the number of diffusions tends to infinity. We prove that th…
math.PR2010★ 27 cited
Competing particle systems evolving by interacting Lévy processes
Mykhaylo Shkolnikov
We consider finite and infinite systems of particles on the real line and half-line evolving in continuous time. Hereby, the particles are driven by i.i.d. Lévy processes endowed w…