Transition density estimates for Brownian motion on affine nested fractals

DOI10.1007/BF02099425zbMath0853.60062OpenAlexW2044820665MaRDI QIDQ1338881

Takashi Kumagai, Benjamin M. Hambly, Patrick J. Fitzsimmons

Publication date: 18 December 1994

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02099425

zbMATH Keywords

Brownian motion Dirichlet form Nash-type inequality nested fractals

Mathematics Subject Classification ID

Brownian motion (60J65) Applications of statistical mechanics to specific types of physical systems (82D99)

Related Items

Estimates for the resolvent kernel of the Laplacian on p.c.f. self-similar fractals and blowups, Estimates of transition densities for Brownian motion of nested fractals, Large deviations for Brownian motion on the Sierpiński gasket, Upper estimates of heat kernels for non-local Dirichlet forms on doubling spaces, Fluctuation of the transition density for Brownian motion on random recursive Sierpiński gaskets., Heat kernels on metric measure spaces and an application to semilinear elliptic equations, A Sierpinski carpet like fractal without standard self-similar energy, Two-sided estimates of heat kernels of jump type Dirichlet forms, \(p\)-energies on p.c.f. self-similar sets, Short time asymptotic behaviour and large deviation for Brownian motion on some affine nested fractals, \(L^p\)-Kato class measures for symmetric Markov processes under heat kernel estimates, Brownian motion on a random recursive Sierpinski gasket, Homogenization of nested fractals, Transition probabilities for the simple random walk on the Sierpinski graph, Resistance forms on self-similar sets with finite ramification of finite type, On the equivalence of parabolic Harnack inequalities and heat kernel estimates, Gaps labeling theorem for the bubble-diamond self-similar graphs, Renormalisation of finitely ramified fractals, Density of states for the Anderson model on nested fractals, Estimates of the transition densities for the reflected Brownian motion on simple nested fractals, An elementary proof that walk dimension is greater than two for Brownian motion on Sierpiński carpets, Construction of free quantum fields on nested fractal space-times, Distribution theory on p.c.f. fractals, Nontangential limits and fatou-type theorems on post-critically finite self-similar sets, Spectral asymptotics for \(V\)-variable Sierpinski gaskets, Two-sided estimates of heat kernels on metric measure spaces, Scale-invariant boundary Harnack principle on inner uniform domains in fractal-type spaces, Pseudo-differential operators on fractals and other metric measure spaces, (S)PDE on Fractals and Gaussian Noise, On-diagonal oscillation of the heat kernels on post-critically finite self-similar fractals, On singularity of energy measures for symmetric diffusions with full off-diagonal heat kernel estimates, Harmonic analysis for resistance forms., Heat kernel asymptotics for the measurable Riemannian structure on the Sierpinski gasket, Complex powers of the Laplacian on affine nested fractals as Calderón-Zygmund operators, ASYMPTOTICS FOR THE SPECTRAL AND WALK DIMENSION AS FRACTALS APPROACH EUCLIDEAN SPACE, Local limit theorems for sequences of simple random walks on graphs, Log-periodic asymptotic expansion of the spectral partition function for self-similar sets, Nonlinear diffusion equations on unbounded fractal domains, The resolvent kernel for PCF self-similar fractals, Heat kernel estimates and parabolic Harnack inequalities on graphs and resistance forms, Nonlinear diffusion equations on bounded fractal domains, Equivalence conditions for on-diagonal upper bounds of heat kernels on self-similar spaces, On singularity of energy measures on self-similar sets, Kato class measures of symmetric Markov processes under heat kernel estimates, Geometry of self-similar measures on intervals with overlaps and applications to sub-Gaussian heat kernel estimates, Smooth bumps, a Borel theorem and partitions of smooth functions on p.c.f. fractals, Existence and uniqueness of diffusions on the Julia sets of Misiurewicz-Sierpinski maps, Besov class via heat semigroup on Dirichlet spaces. III: BV functions and sub-Gaussian heat kernel estimates, Regularity of the solutions to SPDEs in metric measure spaces, Renormalization contracts on nested fractals., Localized upper bounds of heat kernels for diffusions via a multiple Dynkin-Hunt formula, Pure point spectrum for the Laplacian on unbounded nested fractals, Boundary Harnack inequality for Markov processes with jumps, On singularity of energy measures for symmetric diffusions with full off-diagonal heat kernel estimates. II: Some borderline examples, Parabolic type equations associated with the Dirichlet form on the sierpinski gasket, The Dirichlet heat kernel in inner uniform domains in fractal-type spaces, Modelling transport in disordered media via diffusion on fractals.

Cites Work