Jürgen Gärtner

From left: Charles Newman, Stanislav Molchanov, Jürgen Gärtner, Oberwolfach 2003

Jürgen Gärtner (* 1950 ) is a German mathematician ( stochastics , analysis ) and university lecturer at the TU Berlin .

Gärtner received his doctorate from Mark Freidlin at Lomonossow University in 1976 ( On the logarithmic asymptotics of large deviation probabilities ). In 1984 he completed his habilitation in Berlin (dissertation B: On the propagation of wavefronts for reaction-diffusion equations). He was at the Academy of Sciences of the GDR in Berlin and is a professor at the TU Berlin.

He made important contributions to the theory of large deviations (Large Deviation Principle, LDP), the KPP equation (1982), LDP for McKean-Vlasov processes (1987 to 1989 with Don Dawson ) and the parabolic Anderson model (with Stanislaw Alexejewitsch Moltschanow , from 1990) and his intermittent behavior. In 1977 he proved a general form of Cramér's Theorem in LD theory, known as Gärtner-Ellis LDP ( Richard S. Ellis proved a weaker proof in 1984). In 1987 he and Don Dawson introduced the construction of a projective limes in the LDP.

In 1994 he was invited to speak at the International Congress of Mathematicians in Zurich (Parabolic systems in random media and aspects of intermittency).

Fonts (selection)

On the asymptotic behavior of the first exit time from a domain. Theory probab. Appl., Vol. 20, 1975, pp. 169-174
On the logarithmic asymptotics of large deviation probabilities. Dissertation, Moscow, 1976.
Theorems on large deviations for a certain class of random processes. Theory probab. Appl., Vol. 21, 1976, pp. 95-106
On large deviations from the invariant measure. Theory probab. Appl., Vol. 22, 1977, pp. 24-39.
Location of wave fronts for the multidimensional KPP equation and Brownian first exit densities. Math. Nachr., Vol. 105, 1982, pp. 317-351
with Dawson: Large deviations and tunneling for particle systems with mean field interaction. CR Math. Rep. Acad. Sci. Canada, Vol. 8, 1986, pp. 387-392
with DA Dawson: Large deviations from the McKean-Vlasov limit for weakly interacting diffusions. Stochastics, Vol. 20, 1987, pp. 247-308
with DA Dawson: Long-time fluctuations of weakly interacting diffusions. In HJ Engelbert, W. Schmidt (Ed.) Stochastic Differential Systems, Springer, 1987, pp. 3-10
with DA Dawson: Long time behavior of interacting diffusions. In JR Norris, editor, Stochastic Calculus in Application. Proc. Cambridge Symp., 1987, Longman, 1988, pp. 29-54
with Don Dawson: Large deviations, free energy functional and quasi-potential for a mean field model of interacting diffusions. Mem. Amer. Math. Society, Volume 78, 1989
with S. Molchanov: Parabolic problems for the Anderson model. I. Intermittency and related topics. Commun. Math. Phys., Vol. 132, 1990, pp. 613-655, Part II, Second-order asymptotics and structure of high peaks. Probab. Theory Relat. Fields, Vol. 111, 1998, pp. 17-55
with S. Molchanov, W. Kanig: Geometric characterization of intermittency in the parabolic Anderson model, Annals of Probability, Volume 35, 2007, pp. 439-499
with W. König: The parabolic Anderson model. In JD. Deuschel, A. Greven, eds., Interacting Stochastic Systems, 2005, pp. 153-179
with F. den Hollander: Intermittency in a catalytic random medium. Annals of Probability, Volume 34, 2006, pp. 2219-2287
with S. Molchanov, W. König: Geometric characterization of intermittency in the parabolic Anderson model, Annals of Probability, Volume 35, 2007, pp. 439-499

Web links

Homepage
Conference for the 60th birthday 2010 (with appreciation from Frank den Hollander)

Individual evidence

↑ The English title appears like this in his list of publications on his website. See also: Jürgen Gärtner in the Mathematics Genealogy Project (English)
↑ Stochastic differential equations for interacting particles, which are described in molecular field approximation, named after the Vlasov equations of plasma physics by Anatoli Alexandrowitsch Wlasow and the stochastic model introduced by Henry McKean (1966)

personal data
SURNAME	Gardener, Jürgen
BRIEF DESCRIPTION	German mathematician
DATE OF BIRTH	1950

[1] The English title appears like this in his list of publications on his website. See also: Jürgen Gärtner in the Mathematics Genealogy Project (English)

[2] Stochastic differential equations for interacting particles, which are described in molecular field approximation, named after the Vlasov equations of plasma physics by Anatoli Alexandrowitsch Wlasow and the stochastic model introduced by Henry McKean (1966)