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What is a stochastic process ? Why learn it?
This has been best explained by Obama in the video in the right side/below. Simply put, it is a random process. There are a lot of real life example of stochastic processes that we encounter, like you searching randomly for your lost smartphone, tossing a coin to decide who will go first etc. What I think, every process that we can imagine of is random within a certain time scale. For example, you go to lunch at 1 P.M. everyday. But if I ask at what minutes and what seconds exactly, that has to be random. Thus we need to have a in depth understanding of stochastic processes.
Stochastic resetting: What and why? An illustrative example.
Stochastic resetting: What and why? An illustrative example.
"Start again, this time you may be successful" - this is not only a Grandfather's advice but also a Physicist's way of handling random stuff, and can be mathematically proven to be effective! When you randomly search for something, it is highly possible that you are going in a completely wrong direction from where you should go actually. Thus restarting again can prevent you from being lost forever where there is no hope of target finding. But restarting too much is not good though as it does not even allow you to take any step towards the target. So what to do then? I study stochastic process under resetting so that I can answer this question.
Fig: Suppose you are searching for some hidden treasures (target - in the figure) around your home. You start searching for it here and there (the green lines being your trajectory). Some days you will be lucky to find the treasures and have a party. However, many days will be there when your search may be fruitless and then being exhausted you need to come back home (the dashed line) empty-handed. You take some rest in your home and start searching the next day. In scientific language, this is called `'resetting', that you come back to the starting position and restart again.
You can ask, why did you need to reset or come back home? The answer is, simply to enhance the search efficiency (so you do not kill yourself being lost in some jungle far away from your some or die out of hunger). Thus 'restarting' is not always bad. But can you prove that mathematically? Yes, and there comes my research on `stochastic resetting'.
I am working on
I am working on
The subject of stochastic resetting is being studied recently in a rigorous fashion due to its paramount application in physics, chemistry and biology. Still, a myriad of ideas flourish everyday on the effect of resetting in any stochastic process. It is a mere process of restarting the dynamics of a system. You wait up to some time for a process to complete, but if it fails to do so start all over again. Any stochastic process when subjected to resetting can exhibit a dramatic change in behavior. It has been observed that restart can actually expedite the completion time of a stochastic process. For example, a foraging animal searching for food in a jungle. If it fails to find food in the daylight it returns to its shelter and starts the search the next day. In a computer algorithm for search of the global minima of a system, one can be forever stuck in a local minima and stay there forever. Thus restarting the algorithm in a new search direction may help get out of that. In a chemical process, restart corresponds to unbinding of the substrate from the enzyme. In defiance of its simple and recurrent application, little is known on a quantitative level on how much resetting is necessary for it to be beneficial.
One paradigmatic example of a process-restart mechanism is the diffusion of a Brownian particle inherited to resetting. After certain random epochs, the particle is returned to its starting position. One quintessential feature of this system is the emergence of non-equilibrium steady state. Also, the first passage properties of the system are also seen to have dramatic consequences when resetting is introduced. We are currently studying that.
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
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)
5) Organizers: Statistical Physics Journal Club, IMSc
6) Student representative in the computer committee, IMSc
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