Abstract:
This paper studies the asymptotic behaviour as t→0 of the transition density of a diffusion process on a smooth manifold. The results are stated in the language of differential geometry. We look at applications of the asymptotic formulae to the local structure of diffusion processes and to spectral theory.
This publication is cited in the following 156 articles:
V. D. Konakov, S. Menotstsi, “Predelnye teoremy dlya sluchainykh bluzhdanii
v giperbolicheskom prostranstve”, Matem. zametki, 117:3 (2025), 402–421
V. G. Danilov, “Asymptotics of Fundamental Solutions of Parabolic Problems”, Math. Notes, 115:2 (2024), 182–191
V. P. Passekov, “On Stabilizing the Rate of Isonymy Divergence”, Russ J Genet, 60:12 (2024), 1719
Pavel Castro-Villarreal, César O. Solano-Cabrera, Ramón Castañeda-Priego, “Covariant description of the colloidal dynamics on curved manifolds”, Front. Phys., 11 (2023)
Toshihiro Yamada, “A new algorithm for computing path integrals and weak approximation of SDEs inspired by large deviations and Malliavin calculus”, Applied Numerical Mathematics, 187 (2023), 192
Stefano Pagliarani, Sergio Polidoro, “A Yosida's parametrix approach to Varadhan's estimates for a degenerate diffusion under the weak Hörmander condition”, Journal of Mathematical Analysis and Applications, 517:1 (2023), 126538
Sonia Mazzucchi, Valter Moretti, Ivan Remizov, Oleg Smolyanov, “Chernoff approximations of Feller semigroups in Riemannian manifolds”, Mathematische Nachrichten, 296:3 (2023), 1244
Xin Chen, Xue-Mei Li, Bo Wu, “Logarithmic heat kernel estimates without curvature restrictions”, Ann. Probab., 51:2 (2023)
Dmitri Alekseevsky, “Microsaccades, Drifts, Hopf Bundle and Neurogeometry”, J. Imaging, 8:3 (2022), 76
M. Aizenman, B. R. Vainberg, I. Ya. Goldsheid, S. Ya. Zhitomirskaya, L. A. Pastur, A. Klein, V. D. Konakov, M. Cranston, B. Simon, V. Jakšić, “Stanislav Alekseevich Molchanov (on his 80th birthday)”, Russian Math. Surveys, 76:5 (2021), 943–949
Adam Nowak, Peter Sjögren, Tomasz Z. Szarek, “Genuinely sharp heat kernel estimates on compact rank-one symmetric spaces, for Jacobi expansions, on a ball and on a simplex”, Math. Ann., 381:3-4 (2021), 1455
Inés Cavero-Peláez, Prachi Parashar, K. V. Shajesh, “Quantum Vacuum Energy of Self-Similar Configurations”, Universe, 7:5 (2021), 128
Lu Li, Zhen Lei Zhang, “On Li-Yau Heat Kernel Estimate”, Acta. Math. Sin.-English Ser., 37:8 (2021), 1205
François Ledrappier, Seonhee Lim, “Local limit theorem in negative curvature”, Duke Math. J., 170:8 (2021)
Weicong Su, “On the peaks of a stochastic heat equation on a sphere with a large radius”, Electron. J. Probab., 25:none (2020)
Xi Chen, Andrew Hassell, “The heat kernel on asymptotically hyperbolic manifolds”, Communications in Partial Differential Equations, 45:9 (2020), 1031
G. Calvaruso, G. Metafune, L. Negro, C. Spina, “Optimal kernel estimates for elliptic operators with second order discontinuous coefficients”, Journal of Mathematical Analysis and Applications, 485:1 (2020), 123763
Supurna Sinha, “Orientational probability distribution of an active Brownian particle: an analytical study”, J. Stat. Mech., 2020:8 (2020), 083201
Vladimir V. Konotop, Evgeny Lakshtanov, Boris Vainberg, “Designing lasing and perfectly absorbing potentials”, Phys. Rev. A, 99:4 (2019)
Balázs Endre Szigeti, Gábor Homa, Zoltán Zimborás, Norbert Barankai, “Short-time behavior of continuous-time quantum walks on graphs”, Phys. Rev. A, 100:6 (2019)