4 papers
Convergence rates for rank-based models with applications to portfolio theory
Tomoyuki Ichiba, Soumik Pal, Mykhaylo Shkolnikov
We determine rates of convergence of rank-based interacting diffusions and semimartingale reflecting Brownian motions to equilibrium. Convergence rate for the total variation metri…
Large volatility-stabilized markets
Mykhaylo Shkolnikov
We investigate the behavior of systems of interacting diffusion processes, known as volatility-stabilized market models in the mathematical finance literature, when the number of d…
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…
Metastability in the generalized Hopfield model with finitely many patterns
Mykhaylo Shkolnikov
This paper continues the study of metastable behaviour in disordered mean field models initiated in [2], [3]. We consider the generalized Hopfield model with finitely many independ…