Shaibal Karmakar
I am a third year Ph.D student at TIFR-ICTS , advised by Anirban Basak.
Previously, I completed my M.Math and B.Math from Indian Statistical Institute, Bengaluru .
My research interest lies in Probability theory and its applications. I have been recently working on the upper tail probability of subgraph counts in Erdős–Rényi random graphs.
I can be reached by email at shaibal.karmakar@icts.res.in.
Research School attended: Mathematical foundations of network models and their applications.- Research School. (Dec 9-13, 2024)
Workshops attended: Mathematical Foundations of Network Models and their Applications (24w4004) (Dec 16-20, 2024)
Project Reports Submitted:
Semester(Jan-Apr 2025) Research Project submitted on 5th May, 2024 Derived the structure of G(n,p) conditioned on the upper tail event of subgraph counts in the localized regime. Also established the rate function of the upper tail event for star counts in one boundary case (left open before) and also computed the corresponding conditional structure of G(n,p) in the full localized regime. Performed a brief review of the upper tail problem in the setting of random regular graphs.
Semester(Aug-Dec 2024) Research Project submitted on 20th December, 2024. Established the rate function of the upper tail large deviation of the subgraph counts of r-armed star graph in Erdős-Rényi random graph G(n, p) on n vertices with edge probability p.
Summer(May-Jul 2024) Research Project submitted on 6th August, 2024. Showed that the rate function of the upper tail large deviation of the subgraph counts of irregular graphs (with maximum degree ∆) in G(n, p) is given by the solution to a mean-field variational problem in the threshold n^(−1/∆) ≪ p ≪ 1.
Semester(Jan-Apr 2024) Research Project submitted on 23rd May, 2024. Performed a literature review of the article 'Upper tails via high moments and entropic stability ' authored by Harel, Mousset and Samotij and extended Theorem 1.6 to a bigger class of graphs, namely "strongly balanced" graphs.
