The Abel Prize pp 289-314 | Cite as
A Personal Perspective on Raghu Varadhan’s Role in the Development of Stochastic Analysis
Abstract
I know Raghu Varadhan professionally but not personally—that is to say we have attended some of the same conferences and Oberwolfach meetings, and even the odd meal while waiting for trains home. Still, it is obvious to me, and I am sure to anyone else who comes close, that he is a person of great humanity who generates warmth and humour whenever he is in the room. A few months after the award of Fields Medals to Werner, Okounkov and Tao in Madrid, Varadhan and I were both in a group of mathematicians talking about the event. I remember clearly Varadhan’s concise summary of the business as “A great day for the coin flippers”. It certainly was: all three used probability in their ground-breaking work and, for the first two, Stochastic Analysis has been a decisive part of their mathematical toolbox. We were all excited that stochastic ideas were having such a substantial effect across areas as far apart as conformal field theory, geometry and number theory. We were also delighted that these achievements were recognized. To me, Varadhan’s remark seemed to capture his modesty and humour rather well. Surely it was another excellent day for the coin flippers when Varadhan was awarded the Abel Prize.
Mathematics Subject Classification (2000)
00-02 00A15 01A70Preview
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References
- 1.Barlow, M.T.: Heat kernels and sets with fractal structure. Contemp. Math. 338, 11–40 (2003) MathSciNetCrossRefGoogle Scholar
- 2.Barlow, M.T., Bass, R.F., Kumagai, T., Teplyaev, A.: Uniqueness of Brownian motion on Sierpinski carpets. arXiv:0812.1802v1 (2008)
- 3.Bismut, J.-M.: Mécanique aléatoire. Lecture Notes in Mathematics, vol. 866. Springer, Berlin (1981). With an English summary zbMATHGoogle Scholar
- 4.Donsker, M.D., Varadhan, S.R.S.: Asymptotic evaluation of certain Markov process expectations for large time. I. Commun. Pure Appl. Math. 28, 1–47 (1975) MathSciNetCrossRefGoogle Scholar
- 5.Donsker, M.D., Varadhan, S.R.S.: Asymptotic evaluation of certain Markov process expectations for large time. II. Commun. Pure Appl. Math. 28, 279–301 (1975) MathSciNetCrossRefGoogle Scholar
- 6.Donsker, M.D., Varadhan, S.R.S.: Asymptotic evaluation of certain Wiener integrals for large time. In: Functional Integration and Its Applications, Proc. Internat. Conf., London, 1974, pp. 15–33. Clarendon Press, Oxford (1975) Google Scholar
- 7.Donsker, M.D., Varadhan, S.R.S.: Asymptotic evaluation of certain Markov process expectations for large time. III. Commun. Pure Appl. Math. 29(4), 389–461 (1976) MathSciNetCrossRefGoogle Scholar
- 8.Donsker, M.D., Varadhan, S.R.S.: Asymptotic evaluation of certain Markov process expectations for large time. IV. Commun. Pure Appl. Math. 36(2), 183–212 (1983) MathSciNetCrossRefGoogle Scholar
- 9.Nadirashvili, N.: Nonuniqueness in the martingale problem and the Dirichlet problem for uniformly elliptic operators. Ann. Sc. Norm. Super. Pisa, Cl. Sci. (4) 24(3), 537–549 (1997) MathSciNetzbMATHGoogle Scholar
- 10.Nirenberg, L.: A strong maximum principle for parabolic equations. Commun. Pure Appl. Math. 6, 167–177 (1953) MathSciNetCrossRefGoogle Scholar
- 11.Sipilainen, E.-M.: A pathwise view of solutions of stochastic differential equations. PhD thesis, University of Edinburgh (1993) Google Scholar
- 12.Stroock, D.W., Varadhan, S.R.S.: Diffusion processes with continuous coefficients. I. Commun. Pure Appl. Math. 22, 345–400 (1969) MathSciNetCrossRefGoogle Scholar
- 13.Stroock, D.W., Varadhan, S.R.S.: Diffusion processes with continuous coefficients. II. Commun. Pure Appl. Math. 22, 479–530 (1969) MathSciNetCrossRefGoogle Scholar
- 14.Stroock, D.W., Varadhan, S.R.S.: Diffusion processes with boundary conditions. Commun. Pure Appl. Math. 24, 147–225 (1971) MathSciNetCrossRefGoogle Scholar
- 15.Stroock, D.W., Varadhan, S.R.S.: On the support of diffusion processes with applications to the strong maximum principle. In: Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Univ. California, Berkeley, CA, 1970/1971. Probability Theory, vol. III, pp. 333–359. Univ. California Press, Berkeley (1972) Google Scholar
- 16.Varadhan, S.R.S.: Asymptotic probabilities and differential equations. Commun. Pure Appl. Math. 19, 261–286 (1966) MathSciNetCrossRefGoogle Scholar
- 17.Varadhan, S.R.S.: Diffusion processes in a small time interval. Commun. Pure Appl. Math. 20, 659–685 (1967) MathSciNetCrossRefGoogle Scholar
- 18.Varadhan, S.R.S.: On the behavior of the fundamental solution of the heat equation with variable coefficients. Commun. Pure Appl. Math. 20, 431–455 (1967) MathSciNetCrossRefGoogle Scholar
- 19.Varadhan, S.R.S.: Stochastic processes. Notes based on a course given at New York University during the year 1967/68. Courant Institute of Mathematical Sciences, New York University, New York (1968) Google Scholar
- 20.Varadhan, S.R.S.: Boundary value problems with rapidly oscillating random coefficients. In: Random Fields, Vols. I, II, Esztergom, 1979. Colloq. Math. Soc. János Bolyai, vol. 27, pp. 835–873. North-Holland, Amsterdam (1981) Google Scholar