Home Page of Subhro Ghosh
Subhroshekhar Ghosh
Princeton University
Sherrerd Hall, Charlton Street
Princeton, NJ 08544
Email: subhrowork (**at**) gmail.com
sg18 (**at**) princeton.edu
Phone: 1-510-409-6693
CV | Research | Teaching
About me
I am a post doc at Princeton University. My mentor at Princeton is Ramon van Handel. Before this, I obtained my PhD in Mathematics at the University of California, Berkeley, in May 2013 under the supervision of Yuval Peres. Earlier, I obtained my Bachelor in Statistics and Master in Mathematics degrees at the Indian Statistical Institute.
My interests lie broadly at the interface of probability, analysis and applications, and I am excited to explore most questions at this juncture. More specifically, I have been interested in:
- Random series
- Random polynomials and their zeroes
- Determinantal processes
- Large deviations
- Stochastic geometry
- Random sets in statistics and learning theory
- Random phenomena in applied harmonic analysis
Research
Here is an overview of my research. Listed below are my papers and preprints.
- Conditional intensity for Gaussian zeroes with a hole: large deviations and a gap,
with A. Nishry,
submitted
preprint
- Rigidity and Tolerance in point processes: Gaussian zeroes and Ginibre eigenvalues, with Y. Peres,
Duke Mathematical Journal, to appear
preprint
- Determinantal processes and completeness of random exponentials: the critical case
Probability Theory and Related Fields, 163 (3-4), 643-665
preprint
- Palm measures and rigidity phenomena in point processes,
Electronic Communications in Probability, to appear
preprint
- Large deviations for zeros of random polynomials with i.i.d. exponential coefficients, with O. Zeitouni,
Int. Math. Res. Not., 2016 (5), 1308-1347
preprint
- Continuum Percolation for Gaussian zeroes and Ginibre eigenvalues, with M. Krishnapur and Y. Peres,
Annals of Probability, 44 (5), 3357-3384
preprint
- Number rigidity in superhomogeneous random point fields , with J. L. Lebowitz,
Journal of Statistical Physics (Special Issue dedicated to Ruelle and Sinai), to appear
preprint
- Fluctuations, large deviations and rigidity in hyperuniform systems: a brief survey, with J.L. Lebowitz,
submitted
preprint
- Multivariate CLT follows from strong Rayleigh property, with T. Liggett and R. Pemantle,
ANALCO 2017, accepted
preprint
- Symmetry of Bound and Antibound States in the Semiclassical Limit for a General Class of Potentials, with S. Dyatlov,
Proc. Amer. Math. Soc. 138 (2010), 3203-3210
preprint
- Exact quantum algorithm to distinguish Boolean functions of different weights , with S.L. Braunstein, B.S. Choi and S. Maitra,
Journal of Physics A: Mathematical and Theoretical, Volume 40, Number 29
journal
- Rigidity and Tolerance in Gaussian zeroes and Ginibre eigenvalues: quantitative estimates
preprint
- Rigidity hierarchy in random point fields: random polynomials and determinantal
processes , with M. Krishnapur,
preprint
- Random gap and density theorems, with T. Austin,
draft available upon request.
We show that for any ergodic point process of critical intensity 1 on the real line, the exponentials corresponding to the random frequencies from the point process span $L^2(-\pi,\pi)$, thereby answering a question of Lyons. We also show that the density-completeness correspondence breaks down when we consider completeness in sets (or, more generally, measures) other than an interval. Finally, we study random Gram determinants arising from such random exponential functions, in comparison to the classic Szego limit theorems.
- Notes on tolerance for point processes , with M. Krishnapur,
draft available upon request.
A Random Gallery
Left to right: Poisson point process, Ginibre eigenvalues and Gaussian zeroes
Left to right: Surface plot of a normalised GAF, Linear rigidity of Ginibre eigenvalues
Left to right: Conditional intensity for a Gaussian matrix and for a Gaussian polynomial
Teaching
In Fall 2014, I gave a series of lectures on determinantal processes, strongly Rayleigh measures, and their concentration phenomena at the Stochastic Analysis Seminar at Princeton.
In Spring 2014, I taught graduate Stochastic Calculus (ORF527).
At Berkeley, I have been a GSI for graduate Probability (Stat 205 A and B), graduate Theoretical Statistics (Stat 210A) and undergrad calculus.