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We review some recent results on connections between Brownian motion, Whittaker functions, random matrices and representation theory.
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Ph. Biane, Ph. Bougerol and N. O’Connell. Littelmann paths and Brownian paths. Duke Math. J
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A. Gerasimov, S. Kharchev, D. Lebedev and S. Oblezin. On a Gauss-Givental representation of quantum Toda chain wave equation. Int. Math. Res. Notices
2006
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T. Ishii and E. Stade. New formulas for Whittaker functions on G L ( n , ℝ ) GL(n,{\mathbb{R}}) . J. Funct. Anal
2007
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J. Moriarty and N. O’Connell. On the free energy of a directed polymer in a Brownian environment. Markov Process. Related Fields
2007
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A. Gerasimov, D. Lebedev and S. Oblezin. Baxter Operator and Archimedean Hecke Algebra. Commun. Math. Phys
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A. N. Kirillov. Introduction to tropical combinatorics. Physics and Combinatorics. Proc. Nagoya 2000 2nd Internat.Workshop
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N. O’Connell and M. Yor. Brownian analogues of Burke’s theorem. Stoch. Process. Appl
2001
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E. Stade. Mellin transforms of G L ( n , ℝ ) GL(n,{\mathbb{R}}) Whittaker functions. Amer. J. Math
2001
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Ph. Bougerol and Th. Jeulin. Paths in Weyl chambers and random matrices. Probab. Th. Rel. Fields
2002
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E. Stade. Archimedean L L -factors on G L ( n ) × G L ( n ) GL(n)\times GL(n) and generalized Barnes integrals. Israel J. Math
2002
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D. Joe and B. Kim. Equivariant mirrors and the Virasoro conjecture for flag manifolds. Int. Math. Res. Notices
2003
Cited alongside, same era.
N. O’Connell. A path-transformation for random walks and the Robinson-Schensted correspondence. Trans. Amer. Math. Soc
2003
Cited alongside, same era.
Ph. Biane, Ph. Bougerol and N. O’Connell. Continuous crystals and Duistermaat-Heckman measure for Coxeter groups. Adv. Math
2009
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A. Gerasimov, D. Lebedev and S. Oblezin. On q q -Deformed Whittaker Function I. Commun. Math. Phys
2010
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T. Seppäläinen and B. Valkó. Bounds for scaling exponents for a 1+1 dimensional directed polymer in a Brownian environment. Alea
2010
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F. Baudoin and N. O’Connell. Exponential functionals of Brownian motion and class one Whittaker functions. Ann. Inst. H. Poincaré Probab. Statist
2011
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M. Katori. O’Connell’s process as a vicious Brownian motion. Phys. Rev. E
2011
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R. Chhaibi. Modèle de Littelmann pour cristaux géométriques, fonctions de Whittaker sur des groupes de Lie et mouvement brownien
2012
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A. Gerasimov, D. Lebedev and S. Oblezin. New Integral Representations of Whittaker Functions for Classical Lie Groups. Russ. Math. Surv
2012
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A. Gorsky, S. Nechaev, R. Santachiara and G. Schehr. Random ballistic growth and diffusion in symmetric spaces. Nucl. Phys. B
2012
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M. Katori. Survival probability of mutually killing Brownian motions and the O’Connell process. J. Stat. Phys
2012
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N. O’Connell. Directed polymers and the quantum Toda lattice. Ann. Probab
2012
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