Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 30 for “"Heat kernel"”.
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Renormierungsgruppen-Flussgleichungen im Heat-Kernel-Formalismus
… untersucht. Dazu benutzen wir die Methode der Heat-Kernel-RG-Flußgleichungen. Die RG-Skala wird über einen sogenannten Heat-Kernel-cutoff eingeführt, der die effektive Wirkung in der Schwinger-Eigenzeit-Darstellung regularisiert. Der Vorteil dieser Methode besteht darin, daß der …
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Heat kernel estimates on glued spaces
In this thesis, we prove heat kernel estimates in two main contexts: (1) manifolds with ends with mixed Dirichlet and Neumann boundary condition and (2) infinite (countable) graphs satisfying certain properties, which we call book-like graphs. In both of these settings, we start with ''sufficiently …
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The heat kernel for manifolds with conic singularities
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1996.
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Heat kernel estimates for elliptic operators with Robin boundary conditions
… conditions ∂νu + βu = 0. We show that the kernel for the semigroup generated by −A satisfies Gaussian and Hölder Gaussian bounds given domain and coefficients regularities. In particular we show that when the domain is Lipschitz and the principal coefficients are real, then the kernel is …
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On-diagonal heat kernel bounds and volume growth on Riemannian manifolds
We investigate heat kernel estimates of the form $p_{t}(x, x) ≥ c_{x}t^{−α}$, for large enough $t$, where $α$ and $c_{x}$ are positive reals and $c_{x}$ may depend on $x$, on manifolds having at least one end with a polynomial volume growth.
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A geometric description of the heat kernel of the Witten Laplacian and the Cheeger-Müller theorem
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-19 without embargo terms
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On the asymptotic expansion of the trace of the the [sic] heat kernel for a subelliptic operator
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1987.
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Monotonicity Formulas for Diffusion Operators on Manifolds and Carnot Groups, Heat Kernel Asymptotics and Wiener's Criterion on Heisenberg-type Groups
… T</em>), related to the Hessian of the heat kernel, and are able to prove a Poon-type frequency monotonicity formula when taking into account a weighting factor depending on ω. We also give examples of manifolds satisfying <em>C</em>(ω), the most interesting of which includes the …
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Path integrals on manifolds with boundary and their asymptotic expansions
… from physical heuristics that solutions to the heat equation on a Riemannian manifold can be represented by a path integral. However, the problem with such path integrals is that they are notoriously ill-defined. One way to make them rigorous (which is often applied in physics) is …
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Energy methods for nonsymmetric nonlocal operators
… full Harnack inequalities, and two-sided heat kernel estimates, which we obtain by extending recently established nonlocal energy methods. We are able to connect the theory of nonsymmetric nonlocal operators with the important results of Aronson-Serrin, Ladyzhenskaya-Solonnikov-Ural'tceva, …
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Efficient high-order integral equation methods for the heat equation
… for solving the boundary value problems of the heat equation with complex geometries in two and three dimensions. First of all, the classical heat potential theory is applied to convert such problems to Volterra integral equations of the second kind via the heat layer potentials. Some advantages …
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Spectral Geometry for Structural Pattern Recognition
… our first contribution is to investigate the heat kernel embedding as a route to computing geometric characterisations of graphs. The reason for turning to the heat kernel is that it encapsulates information concerning the distribution of path lengths and hence node affinities on the graph. …
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Machine learning methods based on diffusion processes
… of diffusion processes. First, the idea of using heat diffusion on a hypersphere to measure similarity has been previously proposed and tested by computer scientists, demonstrating promising results based on a heuristic heat kernel obtained from the zeroth order parametrix expansion; however, how …
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Homogenization of Random Media: Random Walks, Diffusions and Stochastic Interface Models
… results, in particular scaling limits and heat kernel estimates, for random processes moving in random environments and for stochastic interface models. The first chapter will survey recent research and introduce three models of interest: the random conductance model, the Ginzburg-Landau ∇φ …
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On a pseudodifferential calculus with modest boundary decay condition
… of product type and construction of the heat kernel, is presented.</p>
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Θεωρία προσέγγισης με νόρμες του Lorentz πάνω σε ομάδες του Lie
… are defined on nilpotent Lie groups. When the heat Kernel PT(N) is defined on a general nilpotent Lie group the estimate depends on the value of T i.e. is different for small and large T, hence the need to introduce the new Lorentz spaces which are development in this thesis. Several …
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Spectral functions for generalized piston configurations.
… the derivative at s = 0. Information about the heat kernel coefficients can also be found in the spectral zeta function in the form of residues, which provide an indirect way of finding this geometric information about the manifold and the operator.
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Brownian Motion on Spaces with Varying Dimension
… on its transition density functions (also called heat kernel). These two-sided estimates are of Guassian type. However, we show that the parabolic Harnack inequality fails for such process and the measure on the underlying state space does not satisfy volume doubling property. Brownian motion on …
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Graph diffusions and matrix functions: fast algorithms and localization results
… algorithm for computing the related heat kernel diffusion in constant-time. Finally, we generalize this framework to compute any graph diffusion in constant time.
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