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Time-changes of stochastic processes associated with resistance forms

Autor: Croydon, D. A., Hambly, B. M., Kumagai, T.

Given a sequence of resistance forms that converges with respect to the Gromov-Hausdorff-vague topology and satisfies a uniform volume doubling condition, we show the convergence of corresponding Brownian motions and local times. As a corollary of th

Externí odkaz: http://arxiv.org/abs/1609.02120

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Spectral Asymptotics for $V$-variable Sierpinski Gaskets

Autor: Freiberg, U., Hambly, B. M., Hutchinson, John E.

The family of $V$-variable fractals provides a means of interpolating between two families of random fractals previously considered in the literature; scale irregular fractals ($V=1$) and random recursive fractals ($V=\infty$). We consider a class of

Externí odkaz: http://arxiv.org/abs/1502.00711

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Local limit theorems for sequences of simple random walks on graphs

Autor: Croydon, D. A., Hambly, B. M.

Publikováno v: Potential Analysis 29 (2008), no. 4, 351-389

In this article, local limit theorems for sequences of simple random walks on graphs are established. The results formulated are motivated by a variety of random graph models, and explanations are provided as to how they apply to supercritical percol

Externí odkaz: http://arxiv.org/abs/1210.6194

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Autor: Croydon, D. A., Hambly, B. M.

Publikováno v: Stochastic Processes and their Applications 118 (2008), no. 5, 730-754

We use the random self-similarity of the continuum random tree to show that it is homeomorphic to a post-critically finite self-similar fractal equipped with a random self-similar metric. As an application we determine the mean and almost-sure leadin

Externí odkaz: http://arxiv.org/abs/1210.6190

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