Manjunath Krishnapur
Department of Mathematics
Indian Institute of Science
Contact
Office
N25, Dept. of Mathematics.
Phone
+91-80-2293 3207.
E-mail
manju-att- iisc-dot-ac-dot- in
Education
Ph.D.
2006, University of California, Berkeley.
M.Stat
2001, Indian Statistical Institute, Bangalore, Kolkata.
B.Stat (Hons)
1999, Indian Statistical Institute, Kolkata.
Employment
Associate professor
2013-
Assistant Professor
2009-2013 Indian Institute of Science, Bangalore.
Postdoc
2006-2008, University of Toronto, Canada.
Postdoc
2006, SAMSI and UNC, Chapel Hill.
Papers
Inradius of random lemniscates
(with
Erik Lundberg
and
Koushik Ramachandran
) [
Preprint, arXiv:2301.13424
]
The number of limit cycles bifurcating from a randomly perturbed center
(with
Erik Lundberg
and
Oanh Nguyen
) [
Preprint, arXiv:2112.05672
]
One idea and two proofs of the KMT theorems
[
Preprint, arXiv:2008.03287
]
Random words in free groups, non-crossing matchings and RNA secondary structures
(with
Siddhartha Gadgil
)
Indian J. Pure Appl. Math.
(2022)
[
Preprint, arXiv:2007.12109
]
How Many Modes Can a Mixture of Gaussians with Uniformly Bounded Means Have?
(with
Navin Kashyap
)
Information and Inference:
Volume 11, Issue 2, (2022), 423--434
[
Preprint, arXiv:2005.01580
]
Lower Deviations in $\beta$-ensembles and Law of Iterated Logarithm in Last Passage Percolation.
(with
Riddhipratim Basu
,
Shirshendu Ganguly
and
Milind Hegde
)
Israel Journal of Mathematics
242
, (2021) 291--324
[
Preprint, arXiv:1909.01333
]
A relative anti-concentration inequality.
(with
Sourav Sarkar
)
[
Preprint, arXiv:1612.09045
]
Persistence probabilities in centered, stationary, Gaussian processes in discrete time.
(with
Krishna M.
)
Indian J. Pure Appl. Math.
47
, pages 183--194 (2016)
[
Preprint, arXiv:1506.00753
]
Rigidity hierarchy in random point fields: random polynomials and determinantal processes.
(with
Subhroshekhar Ghosh
)
Communications in Mathematical Physics
,
388
, (2021), 1205--1234
[
Preprint, arXiv:1510.08814
]
Phase Transitions for the Uniform Distribution in the PML Problem and its Bethe Approximation.
(with Chun Lam Chan, Winston Fernandes and
Navin Kashyap
)
SIAM J. Discrete Math.
Volume 31, No. 1, (2017), 597--631,
[
Preprint, arXiv:1510.08814
]
Universality of the Stochastic Airy Operator.
(with
Brian Rider
and
Bálint Virág
)
Communications on Pure and Applied Mathematics
Volume 69, Issue 1, (2016), 145--199,
[
arXiv:1306.4832
]
The Ginibre ensemble and Gaussian analytic functions.
(with
Bálint Virág
)
Int. Math. Res. Not. IMRN
2014, no. 6, (2014), 1441--1464
[
arXiv:1112.2457
]
Lipschitz correspondence between metric measure spaces and random distance matrices.
(with
Siddhartha Gadgil
)
Int. Math. Res. Not. IMRN
2013, no. 24, (2013), 5623--5644
[
arXiv:1110.6333
]
Nodal length fluctuations for arithmetic random waves.
(with
Pär Kurlberg
and
Igor Wigman
)
Ann. Math.
vol. 177, no. 2, (2013), 699--737
[
arXiv:1111.2800
]
The single ring theorem.
(with
Alice Guionnet
and
Ofer Zeitouni
)
Ann. Math.
vol. 174 (2011), 1189--1217
[
arXiv:0909.2214
]
Derivation of an eigenvalue probability density function relating to the Poincare disk.
(with
Peter Forrester
)
J. Phys. A: Math. Theor.
vol. 42 (2009), 385204 [
arXiv:0906.5223
]
Appendix to
Random matrices: Universality of ESDs and the circular law.
(Main authors:
Terence Tao
and
Van Vu
)
Ann. Probab.
38 (2010), 2023--2065. [
arXiv.math.PR/0807.4898
]
From random matrices to random analytic functions.
Ann. Probab.
vol. 37 (2009), no. 1, 314--346
[
arXiv.math.PR/0711.1378
]
Overcrowding estimates for zeroes of Planar and Hyperbolic Gaussian analytic functions.
J. Stat. Phys.
vol. 124 (2006), no. 6, 1399--1423.
[
arXiv.math.PR/0510588
]
Determinantal Processes and Independence.
(with
J.Ben Hough
,
Yuval Peres
and
Bálint Virág
)
Probab. Surv.
vol. 3, 206--229, 2006.
[
arXiv.math.PR/0503110
]
Recurrent graphs where two independent random walks collide finitely often.
(with
Yuval Peres
)
Electron. Comm. Probab.
vol. 9, paper no. 8, 72--81, 2004.
[
arXiv.math.PR/0406487
]
Zeros of Random Analytic Functions
[
arXiv.math.PR/0607504
]
Ph.D. thesis
University of California, Berkeley
.
Spring 2006.
Thesis, Book, Lecture notes
Ph.D. thesis
Zeros of Random Analytic Functions [
arXiv.math.PR/0607504
]
University of California, Berkeley
.
Spring 2006.
Book
Zeros of Gaussian analytic functions and Determinantal point processes
(joint with
J.Ben Hough
,
Yuval Peres
and
Bálint Virág
)
Published by AMS
(American Mathematical Society)
Real and complex zeros of random polynomials and analytic functions
- Lectures given at LPS-VI, Kolkata (Dec 2011).
Measure theory
:
Measure theory
(a full semester course),
Measure theory (as required for probability) A
shorter version
(from an
IST mini-course
), Also
lecture videos
Probability
:
First course in probability and statistics
,
Measure theory (condensed)
,
Basics of probability theory
,
Martingales and Brownian motion
.
Problem sets
:
Problems in measure theory
,
Problems in probability theory
,
Problems on martingales
,
Problems on Brownian motion
Special topics in Probability
:
Random matrix theory
course notes (
An older but quite different version
),
Gaussian processes
course notes,
Anti-concentration
(IITB, Jan 2016),
SLE seminar notes - Part 1
(complex analysis, mainly)
Analysis
:
Topics in analysis
,
Fourier analysis and applications
Recorded lectures
Measure theory
(22 lecture course given in 2021)
Gaussian processes
(33 lecture course given in 2020. Thanks to Ritvik Radhakrishnan for creating this!)
SLE short course (4 lectures)
and
SLE seminar (long)
(Thanks to Ritvik Radhakrishnan again)
Fourier analysis and applications
Students
PhD. students
:
Tulasi Ram Reddy
On Critical Points of Random Polynomials and Spectrum of Certain Products of RandomMatrices
(2016)
Kartick Adhikari
Hole probabilities for determinantal point processes in the complex plane
(2017)
Nanda Kishore Reddy
Eigenvalues of products of random matrices
(2017)
Lakshmi Priya M.E.
Nodal sets of random functions
(2021)
Jnaneshwar Baslingker (in progress)
M.S. thesis students
:
Raghavendra Tripathi (
Determinantal processes and stochastic domination
- 2019)
Indrajit Jana (
Matchings between point processes
- 2012)
Int. PhD. project students
:
Sourish Parag Maniyar (2022), Raghavendra Tripathi (2018), Prateek Kumar Vishwakarma (2017), Indrajit Jana (2011) and Kartick Adhikari (2011)
UG project students
:
Terrence George George (2015), Venkata Ramana (2015), Anamay Chaturvedi (2016), Pranav Nuti (2018), Dhanus Lal (2022)
External students
:
Nishad Bapatdhar (IISER Pune masters thesis (2018)), Ananya Singhal (CBS semester long projects (2021) and (2022)),
Summer students
:
Arundhati Krishnan (basic probability (2009), real analysis (2010)), Sujayam Saha (random matrix theory (2010)), Subhabrata Sen and Pragya Sur (Random walks, mixing times (2011)), Suryateja Gavva (Analytic number theory (2011)), Hitesh Gakhar, Ashish Chandra and Sourav Sarkar (Random walks (2012)), Jigyasa Gaurav (Basic analytic number theory (2012)), Pratyay Datta, Rushil Nagda and Tanya Goyal (2013), Supriya N (Markov chains (2014)), Sourav Sarkar (anti-concentration (2014)), Debatosh Das and Arnab Datta (branching processes (2014)), Soumyo Biswas (continued fractions (2014)), Sanal Prasad (analytic number theory (2014)), Sridhar Venkatesh (analytic number theory (2015)) and Bhavya Teja (random walks (2015)), Sunidhi Taneja and Rameez Qureshi (discrete probability (2016)), Samyak (hyperbolic plane (2016)), Abhratanu Saha (Real analysis (2016)), Sayantan Khan (Fourier analysis (2016)), Prasenjit Dubey (Statistics (2016)), Gaurang Sriramanan (analytic number theory, Primes in P (2017)), Raunak Ray, Siddhaarth Sarkar, Aditya Raut (random walks, mixing times (2017)), Shubhamoy Nandan (weak convergence (2017)), Nishad Bapatdhar (Statistics in high dimensions (2017)), Anirban Basak, Saptarsi Ghosal, Somak Laha and Sayak Chatterjee (Markov chains (2019)), Deep Ghoshal and Arghya Chakraborty (percolation (2019)), Nafia Saleem (basic algebra (2019)), Swarup Pakiriswamy (analytic number theory (2019)), Chinmay S I (random walks (2020)), Aytijhya Saha (data science (2022)), Soham Mallick and Supratik Basu (random polynomials (2022)), Arunava Gantait and Samprit Chakraborty (discrete probability (2022)), Upendra Singh Parmar (Markov chains (2022)), Bijayan Ray (topics in analysis (2022))
Teaching
Current semester:
Probability theory
For a list of past courses, homeworks, exams etc., click on "Teaching" above (For most recent course notes, look under Lecture notes above. What is inside past course homepages may be outdated)
Martingales and Brownian motion
[Spring 2023]
(Also 2020 and 2015)
Probability Theory
[Fall 2022]
(Also in 2020, 2019
Fall 2015
and
Spring 2015
and
Spring 2010
)
Measure and integration
[Spring 2022]
(Also [Spring 2021], [Spring 2020], [Spring 2018])
Fourier analysis with applications
[Fall 2021]
Gaussian processes
[2020] (Also in [Spring 2014])
Topics in analysis
[Spring 2019]
(Also
[Spring 2017]
and
[Fall 2014]
)
Introduction to probability and statistics
[Fall 2018]
(Also
Fall 2016
,
Fall 2013
and Fall 2012)
Random matrix theory
[Fall 2017]
(Also
Spring 2011
)
Probability models
[Fall 2017]
(Also
Fall 2011
)
Problems in Brownian motion
[Spring 2012].
Functional Analysis
[Fall 2010].
Brownian motion
(or is it
this link
?)
[Fall 2009].
A first course in Probability
[Summer 2009].
SLE seminar
[Summer and Fall 2010].
Seminars
Bangalore probability seminar calendar
and
you tube channel
One world probability seminar
Lectures on Probability and Stochastic Processes
Resources for students
Suggested reading for students in probability
Written with myself as a B.Stat/M.Stat student in mind, need not be useful to anyone today.
ISI Bangalore course notes
Some people:
Borcherds
.
Aldous
.
Peres
.
Tsirelson
TIFR lectures on mathematics
OEIS
WolframAlpha
Probabilists in Bangalore
There are probability faculty, students and postdocs at
ICTS
,
ISI
,
TIFR-CAM
,
IIM
and
IISc
Counter by
www.Digits.net