Mykhaylo Shkolnikov

Email:

mshkolni (at) gmail (dot) com

Address:

Department of Statistics
University of California, Berkeley
Berkeley, CA 94720
USA

I'm a postdoctoral fellow in the Statistics Department of UC Berkeley until June 2014; in July 2014 I will be joining the Mathematics Department of Princeton University as an Assistant Professor. In Spring 2012, I was a postdoctoral fellow at MSRI. Before that, I was a PhD student in the Department of Mathematics at Stanford University. My PhD advisor was Amir Dembo

My areas of research are at the interfaces of probability theory, partial differential equations, integrable systems and mathematical finance. Currently, the focus of my research is on systems of interacting Brownian particles arising in the study of dynamics of random matrices and related objects, as well as on probabilistic interpretations of hyperbolic partial differential equations.

More generally, I am interested in stochastic analysis, random matrix theory, large deviations, the concentration of measure phenomenon, stochastic portfolio theory, hydrodynamic limits and rough path theory.


Previous teaching: STAT 20: Introduction to Probability and Statistics (Fall 2013), STAT 134: Concepts of Probability (Fall 2012)

Here you can find a list of my publications, recent talks, collaborators, and my CV



Publications:

1. Shkolnikov, M. (2007). Affine matrix-valued diffusions. Diploma thesis. University of Munich.
2. Shkolnikov, M. (2009). Competing particle systems evolving by i.i.d. increments. Electronic Journal of Probability 14 728-751. 
3. Shkolnikov, M. (2010). Competing particle systems evolving by interacting Levy processes. Annals of Applied Probability 21 1911-1932. 
4. Shkolnikov, M. (2010). Large systems of diffusions interacting through their ranks. Stochastic Processes and Their Applications 122 1730-1747.  
5. Pal, S., Shkolnikov, M. (2010). Concentration of measure for systems of Brownian particles interacting through their ranks. To appear in Annals of Applied Probability.  
6. Farinelli, S., Shkolnikov, M. (2011). Two models for stochastic losses given default. Journal of Credit Risk 8 Paper 4.  
7. Shkolnikov, M. (2011). Large volatility-stabilized markets. Stochastic Processes and Their Applications 123 212-228.  
8. Ichiba, T., Pal, S., Shkolnikov, M. (2013). Convergence rates for rank-based models with applications to portfolio theory. Probability Theory and Related Fields. 156 415-448.  
9. Karatzas, I., Shiryaev, A. N., Shkolnikov, M. (2011). On the one-sided Tanaka equation with drift. Electronic Communications in Probability 16 664-677. 
10. Ichiba, T., Karatzas, I., Shkolnikov, M. (2011). Strong solutions to stochastic equations with rank-based coefficients. Probability Theory and Related Fields 156 229-248.  
11. Shkolnikov, M. (2011). Competing particle systems and their applications. PhD thesis. Stanford University.
12. Shkolnikov, M. (2012). Some universal estimates for reversible Markov chains. Electronic Journal of Probability 18 Article 11.  
13. Shkolnikov, M. (2012). On a non-linear transformation between Brownian martingales. Submitted.
14. Gorin, V., Shkolnikov, M. (2012). Limits of multilevel TASEP and related processes. To appear in Annales de l'Institut Henri Poincare.
15. Gerhold, S., Kleinert, M., Porkert, P., Shkolnikov, M. (2012). Small time central limit theorems for semimartingales with applications. Submitted.
16. Karatzas, I., Pal, S., Shkolnikov, M. (2012). Systems of Brownian particles with asymmetric collisions. Submitted.
17. Aldous, D., Shkolnikov, M. (2012). Fluctuations of martingales and winning probabilities of game contestants. Electronic Journal of Probability 18 Article 47.
18. Dembo, A., Shkolnikov, M., Varadhan, S.R.S., Zeitouni, O. (2012). Large deviations for diffusions interacting through their ranks. To appear in Communications in Pure and Applied Mathematics.  
19. Racz, M.Z., Shkolnikov, M. (2013). Multidimensional sticky Brownian motions as limits of exclusion processes. To appear in Annals of Applied Probability.  
20. Ichiba, T., Shkolnikov, M. (2013). Large deviations for interacting Bessel-like processes and applications to systemic risk. Submitted. 
21. Pal, S., Shkolnikov, M. (2013). Intertwining diffusions and wave equations. Submitted. 
22. Shkolnikov, M., Karatzas, I. (2013). Time-reversal of reflected Brownian motions in the orthant. Submitted. 
23. Gorin, V., Shkolnikov, M. (2014). Multilevel Dyson Brownian motions via Jack polynomials. Submitted. 


Recent talks:

1. Princeton University, January 2014.
2. University of Connecticut, January 2014.
3. Columbia University, January 2014.
4. University of Southern California, January 2014.
5. University of British Columbia, January 2014.
6. University of Maryland, January 2014.
7. Georgia Tech, January 2014.
8. University of Bonn, December 2013.
9. University of Minnesota, December 2013.
10. Carnegie Mellon University, December 2013.
11. Cornell University, November 2013.
12. Carnegie Mellon University, September 2013.
13. Conference on Stochastic Processes and Their Applications (SPA), University of Colorado, Boulder, July 2013.
14. Stanford University, April 2013.
15. University of Michigan, March 2013.
16. Columbia University, March 2013.
17. MIT, March 2013.
18. University of Washington, Seattle, March 2013.
19. University of California, Berkeley, January 2013.
20. AMS meetings, San Diego, January 2013.
21. University of California, Santa Barbara, October 2012.
22. Conference in honor of Ioannis Karatzas, Columbia University. June 2012.
23. Mathematical Sciences Research Institute. April 2012.
24. University of California, Berkeley. March 2012.
25. MAN Institute, Oxford, United Kingdom. February 2012.
26. ETH, Zurich, Switzerland. February 2012.
27. University of Technology, Vienna, Austria. February 2012.
28. QMF 2011 conference, Sydney, Australia. December 2011.
29. University of California, Los Angeles, USA. December 2011.
30. University of California, Irvine, USA. December 2011.
31. University of California, Berkeley, USA. October 2011.
32. New York University, USA. September 2011.
33. Princeton University, USA. September 2011.
34. University of North Carolina/Duke University, USA. September 2011.
35. University of California, San Diego, USA. April 2011.
36. Stanford University, USA. April 2011.
37. University of Washington, Seattle, USA. March 2011.
38. Columbia University, USA. November 2010.
39. École d'Été de Probabilités, Saint-Flour, France. July 2010.
40. EPFL, Lausanne, Switzerland. June 2010.
41. University of California at Berkeley, USA. April 2010.
42. Stanford University, USA. January 2010.
43. ETH, Zurich, Switzerland. July 2009.


Collaborators:

David Aldous, Amir Dembo, Simone Farinelli, Stefan Gerhold, Vadim Gorin, Tomoyuki Ichiba, Ioannis Karatzas, Max Kleinert, Soumik Pal, Piet Porkert, Miklos Z. Racz, Albert N. Shiryaev, S.R.Srinivasa Varadhan, Ofer Zeitouni