My main theme of research is understanding the effects of stochasticity. We know that stochasticity pervades every process in nature. For some processes, it is important and influences the behavior of the system significantly. Whereas for others, we can get away with a deterministic understanding and stochasticity is just a minor detail. Currently I am focusing on effects of stochasticity on ecological systems. Below are more specific examples of my research.
Foraging is a fundamental process in ecology through which energy flows between the different trophic levels. The rate of gathering food sets a number of constraints on the sizes and fitness of animals/consumers existing in a habitat. The fitness is affected by environmental variables like the average amount of food available and it's variability, and also by the foraging strategy employed by the consumer. We study simple models to understand the relationships between the different environmental, behavioral and physiological parameters using the most basic ingredients. We find a number of surprising results that show trade-offs that exist while trying to maximize fitness. For example, we show that greed can both help and hurt depending on spatial dimensions! (PRE2017a). There also exist optimal ways of being frugal (PRE2018) and ignorant (JSTAT2018) to maximize fitness. Our latest model which incorporates more physiological variables also suggest that striking trade-offs exist in investing resources in offsprings, optimizing litter-size and self-preservation (Arxiv). These results are also applicable to a larger class of problems of investment in presence of fluctuating resource availability.
Understanding random walks is fundamental to understanding stochastic processes. Random walks have been studied for over a century and yet there are aspects of the process that are not fully understood. We use random walks and first-passage process principles and tools to model basic stochastic search processes, yielding us non-trivial insights about how fluctuations play a role in search processes. For example, in JSTAT2016 we show that resetting a random-searcher periodically improves search time. Also depending on the steepness of the cost as a function of number of searchers, and the dimension of space, there exists an optimum number of searchers.
Network theory has seen an exponential increase in interest and research over the last few decades. Statistical physics, which traditionally was developed to deal with Euclidean lattices, provides very useful tools to study properties of networks and processes on them. We study simple generative processes that lead to highly clustered networks, and also try to understand the implications these processes have on the connectivity properties of such networks. Specifically, in PRL2016 we show that simple rules inspired by Facebook friendships to generate networks lead to a number of densification transitions. We find a heirarchy of transitions where the network shows prominence in larger and larger cliques. In another work PRE2017b, we develop an analytical tool to compute the sizes of percolating k-cores in networks that are not just trees. These tools are particularly important as most real-world networks are highly clustered in that they contain high density of short cycles.
I am also interested in fundamental processes in discrete probability.