Vol. 15, No. 1, 2022

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 5, 1501–1870
Issue 4, 1127–1500
Issue 3, 757–1126
Issue 2, 379–756
Issue 1, 1–377

Volume 16, 10 issues

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
Editors' interests
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author index
To appear
Other MSP journals
Diffusion in small time in incomplete sub-Riemannian manifolds

Ismael Bailleul and James Norris

Vol. 15 (2022), No. 1, 63–84

For incomplete sub-Riemannian manifolds and for an associated second-order hypoelliptic operator, which need not be symmetric, we identify two alternative conditions for the validity of Gaussian-type upper bounds on heat kernels and transition probabilities, with optimal constant in the exponent. Under similar conditions, we obtain the small-time logarithmic asymptotics of the heat kernel and show concentration of diffusion bridge measures near a path of minimal energy. The first condition requires that we consider points whose distance apart is no greater than the sum of their distances to infinity. The second condition requires only that the operator not be too asymmetric.

sub-Riemannian, heat kernel, diffusion
Mathematical Subject Classification 2010
Primary: 35K08, 58J65, 60J60
Received: 26 April 2019
Revised: 21 February 2020
Accepted: 15 September 2020
Published: 16 March 2022
Ismael Bailleul
CNRS, Institut de Recherche Mathematiques de Rennes, UMR 6625
University of Rennes 1
James Norris
Statistical Laboratory
Centre for Mathematical Sciences
University of Cambridge
United Kingdom