Liouville heat kernel: regularity and bounds
arXiv:1406.0491 · doi:10.1214/15-AIHP676
Abstract
We initiate in this paper the study of analytic properties of the Liouville heat kernel. In particular, we establish regularity estimates on the heat kernel and derive non trivial lower and upper bounds.
49 pages. Journal version
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- Non-universality for first passage percolation on the exponential of log-correlated Gaussian fields
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- Continuity and estimates of the Liouville heat kernel with applications to spectral dimensions
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- Spectral representation of one-dimensional Liouville Brownian Motion and Liouville Brownian excursion
- Heat kernels on 2d Liouville quantum gravity: a numerical study
- Conformally invariant random fields, quantum Liouville measures, and random Paneitz operators on Riemannian manifolds of even dimension
- Localized upper bounds of heat kernels for diffusions via a multiple Dynkin-Hunt formula