Gaussian heat kernel upper bounds via the Phragmén-Lindelöf theorem
نویسندگان
چکیده
منابع مشابه
Gaussian Upper Bounds for the Heat Kernel on Arbitrary Manifolds
The history of the heat kernel Gaussian estimates started with the works of Nash [25] and Aronson [2] where the double-sided Gaussian estimates were obtained for the heat kernel of a uniformly parabolic equation in IR in a divergence form (see also [15] for improvement of the original Nash’s argument and [26] for a consistent account of the Aronson’s results and related topics). In particular, ...
متن کاملThe algebraic surfaces on which the classical Phragmén - Lindelöf theorem holds
Let V be an algebraic variety in Cn . We say that V satisfies the strong Phragmén-Lindelöf property (SPL) or that the classical Phragmén-Lindelöf Theorem holds on V if the following is true: There exists a positive constant A such that each plurisubharmonic function u on V which is bounded above by |z| + o(|z|) on V and by 0 on the real points in V already is bounded by A| Im z|. For algebraic ...
متن کاملHeat Kernel Upper Bounds on Long Range Percolation Clusters
In this paper, we derive upper bounds for the heat kernel of the simple random walk on the infinite cluster of a supercritical long range percolation process. For any d ≥ 1 and for any exponent s ∈ (d, (d + 2) ∧ 2d) giving the rate of decay of the percolation process, we show that the return probability decays like t− /s−d up to logarithmic corrections, where t denotes the time the walk is run....
متن کاملHeat Kernel Upper Bounds for Interacting Particle Systems
We show a diffusive upper bound on the transition probability of a tagged particle in the symmetric simple exclusion process. The proof relies on optimal spectral gap estimates for the dynamics in finite volume, which are of independent interest. We also show off-diagonal estimates of Carne-Varopoulos type. MSC 2010: 82C22, 35B65, 60K35.
متن کاملKernel: Lower and Upper Bounds
Through this lecture note we try to provide a portal into the emerging filed of kernelization. We exhibit through examples various tools to prove both lower and upper bounds on the kernel sizes.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2007
ISSN: 0024-6115
DOI: 10.1112/plms/pdm050