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V. Balakrishnan is a theoretical physicist associated with the Indian Institute of Technology Madras. Its institutional profile identifies research in quantum dynamics, stochastic processes and dynamical systems, including random walks on hierarchical structures and recurrence statistics.^[ref]

His Physical Applications of Stochastic Processes by V. Balakrishnan connects probability calculations to physical motion. A particularly instructive example is the fixed-step isotropic random flight: independent directions give zero mean displacement but a mean squared displacement proportional to the number of steps. Shrinking the step length and duration together then produces a finite diffusion coefficient and a diffusion equation description.^[ref]

The example illustrates a recurring scientific distinction in his exposition: an average position, a typical displacement and a probability density answer different questions. Cancellation of displacement vectors does not eliminate the spreading of individual trajectories. IIT Madras's account of the chair established in his honor also identifies contributions to continuous-time random walks and recurrences in dynamical systems.^[ref]