Geodesic
Parametrix, heat kernel asymptotics, and regularized trace of the diffusion semigroup
Informatics and Automation, Differential equations and topology. II, Tome 271 (2010), pp. 241-258.

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We establish a relationship between a path integral representation of the heat kernel and the construction of a fundamental solution to a diffusion-type equation by the parametrix method; this relationship is used to find the coefficients of a short-time asymptotic expansion of the heat kernel. We extend the approach proposed to the case of diffusion with drift and obtain two-sided estimates for the regularized trace of the corresponding evolution semigroup. 
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S. A. Stepin. Parametrix, heat kernel asymptotics, and regularized trace of the diffusion semigroup. Informatics and Automation, Differential equations and topology. II, Tome 271 (2010), pp. 241-258. http://geodesic.mathdoc.fr/item/TRSPY_2010_271_a16/

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