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KOUSHIK RAMACHANDRAN 
Department of Mathematics
Oklahoma State University
Stillwater, OK- 74074
EMAIL : koushik "dot" ramachandran AT okstate "dot" edu

I am currently a Visiting Assistant Professor at Oklahoma State University. 

During 2014-2015, I was a postdoc working with Siva Athreya in the Stat-Math unit of ISI Bangalore

I graduated with a Ph. D in Mathematics from Purdue University in May 2014. My thesis advisors were Alexandre Eremenko and Svitlana Mayboroda.

RESEARCH INTERESTS 

My research interests are in Complex Analysis, Potential theory, and Probability. I have worked on asymptotic behavior of quantities associated with the Laplacian (e.g Martin kernels, harmonic measures, and exit times of Brownian motion), and general Euclidean potential theory. I am currently thinking about analytic problems with a probabilistic flavor.

PUBLICATIONS 

1) Asymptotic behavior of positive harmonic functions in certain unbounded domains (Potential Analysis, Vol 41, Issue 2, (2014), 383-405).  PDF.

2) (with E. Lundberg) Electrostatic skeletons (Ann. Acad. Sci. Fenn. Math, Vol 40, (2015), 397-401) PDF
  
3) (with I. Pritsker) Equidistribution of Zeros of Random Polynomials (Journal of Approximation theory, Vol 215, (2017), 106-117).  PDF

4) (with S. Athreya) Harnack inequality for non-local Schrodinger operators (Potential Analysis, online first, (2017) DOI : 10.1007/s11118-017-9646-6). PDF

5) (with E. Lundberg) The arclength and topology of a random lemniscate (accepted, Journal of the London Mathematical Society) PDF

6) (with A.-K. Gallagher and J. Lebl) Convexity of level lines of Martin functions and applications (submitted) PDF

7) (with I. Pritsker) Natural boundary and zero distribution of random polynomials in smooth domains (preprint) PDF