Geodesic
Family of instantons of the~Kraichnan model with a~frozen velocity field
Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 2, pp. 200-213

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We find the family of instantons of the Kraichnan model with a frozen velocity field. Using these instantons, we investigate the asymptotic behavior of higher orders of the perturbation theory series constructed for the response function. We demonstrate that although the number of diagrams increases factorially with the degree of the perturbation series term, the perturbation series itself has a finite and sometimes even infinite convergence radius. We thus disprove the commonly accepted view that the type of series convergence can be determined by estimating the number of diagrams in higher orders of the perturbation theory.
Keywords: perturbation theory, higher-order asymptotic behavior, instanton, frozen velocity field.
Mots-clés : Kraichnan model 
@article{TMF_2009_158_2_a2,
     author = {M. V. Komarova and I. S. Kremnev and M. Yu. Nalimov},
     title = {Family of instantons of {the~Kraichnan} model with a~frozen velocity field},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {200--213},
     publisher = {mathdoc},
     volume = {158},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_158_2_a2/}
}
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M. V. Komarova; I. S. Kremnev; M. Yu. Nalimov. Family of instantons of the~Kraichnan model with a~frozen velocity field. Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 2, pp. 200-213. http://geodesic.mathdoc.fr/item/TMF_2009_158_2_a2/