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What is a stochastic process ? Why learn it?
This has been best explained by Obama in the video on the right side/below. Simply put, it is a random process. There are plenty of stochastic processes that we encounter in our day-to-day life. For instance, when you are searching randomly for the lost smartphone/key, tossing a coin to decide who will go first, kicking the football randomly without seeing if there is anyone to receive it, etc. I believe every process we can imagine is random on a certain timescale. For example, you go to lunch at 1 P.M. every day. But if I ask, at what minutes and what seconds exactly, that has to be random. Naively, one might not be bothered so much by such randomness since, unlike Newton's laws, no prediction could be made to exactly determine the process's future. However, one can always predict the future outcome of the process on a proababilistic level with the help of the theory of stochastic processes. For e.g., no one can predict the stock market's movement, yet physicists, economists, and mathematicians greatly rely on the theory of stochastic processes to predict the market's nature. Biological processes such as DNA assembly and RNA transcription have the theory of stochastic processes in their core. Furthermore, the recent development of artificial intelligence (AI) is nothing but a niche application of the theory of stochastic processes. Thus, we need to have an in-depth understanding of stochastic processes.
Stochastic resetting: Imagine searching for a lost item: if you wander aimlessly for too long without success, your best strategy is often to return to your starting point and begin anew. This simple yet profound concept—stochastic resetting—transforms how we understand search processes across nature and technology. While randomly exploring a space guarantees you will eventually find a target, random walks are notoriously prone to drifting off into vast, empty regions, leading to drastically inefficient search times. Resetting acts as a powerful optimization tool that cuts down these times by preventing infinite wandering. In biology and ecology, this framework explains how proteins efficiently locate specific DNA sequences or how animals optimize foraging in unpredictable landscapes. In chemistry, resetting mechanisms can govern reaction rates and catalytic processes. Beyond the natural world, computer scientists apply these principles to streamline randomized search algorithms, while queuing theory uses them to manage network delays by intentionally restarting stalled tasks. By introducing a "restart" button to random motion, we uncover a universal mathematical mechanism that turns fundamentally inefficient wandering into highly optimized exploration.
This visualization below tracks a swarm of particles undergoing random 2D diffusion, where each particle occasionally triggers a return to the origin. By adjusting the sliders, you can observe in real-time how the interplay between the diffusion constant, resetting rate, and return speed shapes the steady-state distribution of the system.
Current members of our group at IMSc with the leader standing behind ;)
Other Activities
Other Activities
1) Reviewer: Physical Review E, Physical Review Letters, Physical Review Research, Chaos
2) Teaching Assistant for the course: Computational Physics, 2023, IMSc. Course instructor: Dr. Sayantan Sharma
3) Teaching Assistant for the course: Stochastic Processes, 2023, 2025, IMSc. Course instructor: Dr. Arnab Pal
4) Volunteered in organizing: IMSc 60 conference (2023), Frontiers in Non-equilibrium Physics conference (2023), Science at the Sabha (2023), Science at the Sabha (2024), Amal Kumar Raychaudhuri Centenary conference (2024), Chennai Soft Matter Days conference (2024)
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