S. R. Srinivasa Varadhan

Varadhan’s trajectory began in Chennai and the Indian Statistical Institute (ISI) in Kolkata, where a culture of mathematics and statistics fed young talent. Early exposure to measure theory, functional analysis, and stochastic processes prepared him for the Courant Institute in New York, where he would spend most of his career. There he met problems that required marrying probability with analysis: how to describe diffusions rigorously; how to quantify unlikely fluctuations; how to pass from microscopic randomness to macroscopic laws. The Stroock–Varadhan theory of diffusion processes addressed a foundational gap. Rather than define a diffusion by a stochastic differential equation with formal coefficients, they posed the martingale problem, specifying the generator and domain, and proved existence and uniqueness under conditions that could be checked. This reframed the subject: PDE methods, semigroup theory, and probabilistic intuition joined into a coherent toolkit. The approach let mathematicians build diffusions corresponding to elliptic operators with measurable coefficients, extending far beyond classical smooth settings. Large deviations—the Donsker–Varadhan program—attacked the tails of probability distributions in path space. Instead of central limit fluctuations, one asks: with what exponential rate do rare events occur? The answer involves a rate function (often related to entropy) and variational principles that resemble mechanics and thermodynamics. Applications span statistical physics (Gibbs measures, phase transitions), queuing networks (buffer overflows), information theory (error exponents), and finance (risk assessment). Varadhan’s contributions include abstract frameworks, concrete computations for Markov processes, and the demonstration that large deviations is not a collection of tricks but a theory with unifying theorems. A third theme is hydrodynamic limits: deriving deterministic PDEs as scaling limits of interacting particle systems. Here again, Varadhan’s taste favored general mechanisms over ad hoc arguments, illuminating how macroscopic transport equations emerge from microscopic randomness. Across these areas his papers display economical proofs and an instinct for the right level of generality. The 2007 Abel Prize recognized this architecture of ideas. Yet colleagues often emphasize something else: a teacher who listens, credits collaborators, and asks questions that clarify without humiliating. His lectures are models of exposition, and his office hours are legendary for patience. In an era of mathematical specialization, Varadhan demonstrates how probability can be a common language across sciences without losing rigor. For students, his work teaches that abstraction is not distance from reality but a means to hold many models at once and see their shared skeleton.