Research Area: Random matrices, Free Probability, Statistics and Random Simplicial Complexes.
Collaborator: Arup Bose, Suman Guha, Rajat Subhra Hazra, Shreela Gangopadhya, Santanu Datta, Kartick Adhikari, Nanda Kishore Reddy, Tulasi Ram Reddy, Indrajit Jana, Alexander Soshnikov, Krishna B. Athreya, Radhendushka Srivastava, Shambhu Nath Maurya, Kiran Kumar A. S..
Publication:
Book:
Random Circulant Matrices. Arup Bose and Koushik Saha. Chapman and Hall, CRC Press, Boca Raton, FL, 2019.
Papers in Journals and Proceedings:
1. Limiting spectral distribution of circulant type matrices with dependent inputs. Electronic Journal of Probability. Vol 14, No. 86, 2463--2491, 2009 (with Arup Bose and Rajat Subhra Hazra)
2. Spectral Norm of Circulant Type matrices with heavy tailed entries. Electronic Communication in Probability, 15, 299--313, 2010 (with Arup Bose and Rajat Subhra Hazra)
3. Spectral Norm of Circulant Type matrices. Journal of Theoretical Probability, Vol. 24, No. 2, 479--516, 2011 (with Arup Bose and Rajat Subhra Hazra)
4. Convergence of joint moments for independent random patterned matrices. Annals of Probability, 39, No. 4, 1607--1620, 2011 (with Arup Bose and Rajat Subhra Hazra)
5. Half independence and half cumulants. Electronic Communication in Probability, 16, 405--422, 2011 (with Arup Bose and Rajat Subhra Hazra)
6. Circulant type matrices with heavy tailed entries. Statistics and Probability Letters, Vol. 81, No. 11, 1706--1716, 2011 (with Arup Bose, Suman Guha and Rajat Subhra Hazra).
7. Poisson Convergence of eigenvalues of circulant type matrices. Extremes, 14, No. 4, 365--392, 2011 (with Arup Bose and Rajat Subhra Hazra).
8. Product of exponentials and spectral radius of k-circulants. Annales de l'Institut Henri Poincare Probabilites et Statistiques, 48, No. 2, 424--443, 2012 (with Arup Bose and Rajat Subhra Hazra).
9. Extremum of Circulant type matrices: a survey. Journal of Indian Statistical Association, 50. No. 1--2, 21--49, 2012 (with Arup Bose and Rajat Subhra Hazra).
10. Patterned Random Matrices and Method of Moments. Proceedings of the International Congress of Mathematicians, Volume IV, 2203--2231, Hindustan Book Agency, New Delhi, 2010 (with Arup Bose and Rajat Subhra Hazra).
11. Convergence of a class of Toeplitz type matrices. Random Matrices: Theory and Applications, 2, no. 3, 2013 (with Arup Boes and Sreela Gangopadhyay).
12. Consistency of multivariate density estimators using random bandwidths. Communications in Statistics: Theory & Methods, 45, no. 2, 252-266, 2016 (with Santanu Datta).
13. Determinantal point processes in the plane from products of random matrices. Annales de l'Institut Henri Poincare Probabilites et Statistiques. 52, no. 1, 16--46, 2016 (with Kartick Adhikari, Nanda Kishore Reddy and Tulasi Ram Reddy).
14. Fluctuations of Linear Eigenvalue Statistics of Random Band Matrices. SIAM: Theory of Probability and its applications, 60, no. 3, 407--443, 2016 (with Indrajit Jana and Alexander Soshnikov).
15. Pointwise and uniform convergence of multivariate kernel density estimators using random bandwidths. Accepted for publication in Communications in Statistics Theory & Methods, 46, no. 6, 2708--2723, 2017 (with Santanu Datta).
16. Fluctuations of eigenvalues of patterned random matrices. Journal of Mathematical Physics, Vol. 58, no. 6, 2017 (with Kartick Adhikari).
17. AR(1) sequence with random coefficients: regenerative properties and its application. Communications on Stochastic Analysis, 11, no. 3, pp. 373-381, 2017 (with Krishna B Athreya and Radhendushka Srivastava).
18. Universality in the fluctuation of eigenvalues of random circulant matrices. Statistics and Probability Letters, Vol. 138, 1-8, 2018 (with Kartick Adhikari).
19. Process convergence of fluctuations of linear eigenvalue statistics of band Toeplitz matrices. Statistics and Probability Letters, Vol. 166, pp 11, 2020 (with Shambhu Nath Maurya).
20. Fluctuations of linear eigenvalue statistics of reverse circulant and symmetric circulant matrices with independent entries. Journal of Mathematical Physics, Vol. 62, no. 4, 2021 (with Shambhu nath Maurya).
21. Process convergence of Fluctuations of linear eigenvalue statistics of random circulant matrices. Random Matrices: Theory and Applications, 10, no. 4, 32 pp, 2021 (with Arup Bose and Shambhu Nath Maurya).
22. Some patterned matrices with independent entries. Random Matrices: Theory and Applications, 10, no. 3, 46 pp, 2021 (with Arup Bose and Priyanka Sen).
Erratum: Some patterned matrices with independent entries. Random Matrices: Theory and Applications, 11, no. 3, 4 pp, 2022 (with Arup Bose and Priyanka Sen).
23. Linear eigenvalue statistics of random matrices with a variance profile. Random Matrices: Theory and Applications, Volume 10, no. 3. 25 pp, 2021 (with Kartick Adhikari and Indrajit Jana).
24. Time dependent fluctuations of linear eigenvalue statistics of some patterned matrices. Journal of Mathematical Physics, Vol. 10, no. 4, 16 pp, 2022 (with Arup Bose and Shambhu Nath Maurya).
25. Random matrices with independent entries: beyond non-crossing partitions. Random Matrices: Theory and Applications, Vol. 11, no. 2. 42 pp, 2022 (with Arup Bose and Priyanka Sen).
26. Linear eigenvalue statistics of XX' matrices. Journal of Mathematical Physics, Vol. 64, no. 12, 16 pp, 2023 (with Shambhu Nath Maurya and Kiran Kumar A. S.).
27. A non-Gaussian limit for linear eigenvalue statistics of Hankel matrices. Random Matrices: Theory and Applications, Vol. 14, no. 3. 28 pp, 2025 (with Shambhu Nath Maurya and Kiran Kumar A. S.).
Link to some probability seminars in India: Bangalore Probability Seminar, Lectures on Probability and Stochastic Processes.