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Gady Kozma is an Israeli mathematician. Kozma obtained his PhD in 2001 at the University of Tel Aviv with Alexander Olevskii.[1] He is a scientist at the Weizmann Institute. In 2005, he demonstrated the existence of the scaling limit value (that is, for increasingly finer lattices) of the loop-erased random walk in three dimensions and its invariance under rotations and dilations.[2]
A loop-erased random walk consists of a random walk, whose loops, which form when it intersects itself, are removed. This was introduced to the study of self-avoiding random walk by Gregory Lawler in 1980,[3] but is an independent model in another universality class. In the two-dimensional case, conformal invariance was proved by Lawler, Oded Schramm and Wendelin Werner (with Schramm–Loewner evolution) in 2004.[4] The cases of four and more dimensions were treated by Lawler, the scale limiting value is Brownian motion, in four dimensions. Kozma treated the two-dimensional case in 2002 with a new method. In addition to probability theory, he also deals with Fourier series.[5]
In 2008 he received the Erdős Prize and in 2010 the Rollo Davidson Prize. He is an editor of the Journal d'Analyse Mathématique.[6]
References edit
- ^ Gady Kozma at the Mathematics Genealogy Project
- ^ Kozma, Gady (2007). "The scaling limit of loop-erased random walk in three dimensions". Acta Mathematica. 199 (1): 29–152. arXiv:math/0508344. doi:10.1007/s11511-007-0018-8.
- ^ Lawler, Gregory F. (September 1980). "A self-avoiding random walk". Duke Mathematical Journal. 47 (3): 655–693. doi:10.1215/S0012-7094-80-04741-9.
- ^ Lawler, Gregory F.; Schramm, Oded; Werner, Wendelin (2004), "Conformal invariance of planar loop-erased random walks and uniform spanning trees", Annals of Probability, 32 (1B): 939–995, arXiv:math.PR/0112234, doi:10.1214/aop/1079021469
- ^ Kozma, Gady; Olevskii, Alexander (2006). "Analytic representation of functions and a new quasi-analyticity threshold". Annals of Mathematics. Second series. 164 (3): 1033–1064. arXiv:math/0406261. Bibcode:2004math......6261K. doi:10.4007/annals.2006.164.1033. S2CID 18052987.
- ^ "Editorial board". Journal d'Analyse Mathématique, homepage at the Hebrew University of Jerusalem. Retrieved 16 October 2022.