Search Results - "Barlow, Martin T."

Non-local Dirichlet forms and symmetric jump processes by Barlow, Martin T., Bass, Richard F., Chen, Zhen-Qing, Kassmann, Moritz

“…We consider the non-local symmetric Dirichlet form (\mathcal {E}, \mathcal {F}) given by \[\mathcal {E} (f,f)=\int \limits _{\mathbb {R}^d} \int \limits…”
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Gaussian bounds and parabolic Harnack inequality on locally irregular graphs by Barlow, Martin T., Chen, Xinxing

“…A well known theorem of Delmotte is that Gaussian bounds, parabolic Harnack inequality, and the combination of volume doubling and Poincaré inequality are…”
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Spectral Dimension and Random Walks on the Two Dimensional Uniform Spanning Tree by Barlow, Martin T., Masson, Robert

“…We study the simple random walk on the uniform spanning tree on . We obtain estimates for the transition probabilities of the random walk, the distance of the…”
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Random Walk on the Incipient Infinite Cluster for Oriented Percolation in High Dimensions by Barlow, Martin T., Járai, Antal A., Kumagai, Takashi, Slade, Gordon

“…We consider simple random walk on the incipient infinite cluster for the spread-out model of oriented percolation on . In dimensions d > 6, we obtain bounds on…”
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Stability of the elliptic Harnack inequality by Barlow, Martin, Murugan, Mathav

“…We prove that the elliptic Harnack inequality (on a manifold, graph, or suitably regular metric measure space) is stable under bounded perturbations, as well…”
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Characterization of sub-Gaussian heat kernel estimates on strongly recurrent graphs by Barlow, Martin T., Coulhoun, Thierry, Kumagai, Takashi

“…Sub‐Gaussian estimates for random walks are typical of fractal graphs. We characterize them in the strongly recurrent case, in terms of resistance estimates…”
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Some Boundary Harnack Principles with Uniform Constants by Barlow, Martin T., Karli, Deniz

“…We prove two versions of a boundary Harnack principle in which the constants do not depend on the domain by using probabilistic methods…”
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Stability of parabolic Harnack inequalities by Barlow, Martin T., Bass, Richard F.

“…Let (G,E) be a graph with weights \{a_{xy}\} for which a parabolic Harnack inequality holds with space-time scaling exponent \beta \ge 2. Suppose \{a'_{xy}\}…”
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BOUNDARIES OF PLANAR GRAPHS, VIA CIRCLE PACKINGS by Angel, Omer, Barlow, Martin T., Gurel-Gurevich, Ori, Nachmias, Asaf

“…We provide a geometric representation of the Poisson and Martin boundaries of a transient, bounded degree triangulation of the plane in terms of its circle…”
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Random Walks on Supercritical Percolation Clusters by Barlow, Martin T.

“…We obtain Gaussian upper and lower bounds on the transition density qt(x,y) of the continuous time simple random walk on a supercritical percolation cluster…”
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Convergence to fractional kinetics for random walks associated with unbounded conductances by Barlow, Martin T., Černý, Jiří

“…We consider a random walk among unbounded random conductances whose distribution has infinite expectation and polynomial tail. We prove that the scaling limit…”
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EXPONENTIAL TAIL BOUNDS FOR LOOP-ERASED RANDOM WALK IN TWO DIMENSIONS by Barlow, Martin T., Masson, Robert

“…Let M n be the number of steps of the loop-erasure of a simple random walk on ${\Bbb Z}^{2}$ from the origin to the circle of radius n. We relate the moments…”
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THE RANDOM CONDUCTANCE MODEL WITH CAUCHY TAILS by Barlow, Martin T., Zheng, Xinghua

“…We consider a random walk in an Cauchy-tailed conductances environment. We obtain a quenched functional CLT for the suitably rescaled random walk, and, as a…”
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Erratum to: Convergence to fractional kinetics for random walks associated with unbounded conductances by Barlow, Martin T., Černý, Jiří

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Coupling and Harnack inequalities for Sierpiński carpets by Barlow, Martin T., Bass, Richard F.

“…Uniform Harnack inequalities for harmonic functions on the pre-and graphical Sierpinski carpets are proved using a probabilistic coupling argument. Various…”
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Parabolic Harnack inequality and heat kernel estimates for random walks with long range jumps by Barlow, Martin T., Bass, Richard F., Kumagai, Takashi

“…We investigate the relationships between the parabolic Harnack inequality, heat kernel estimates, some geometric conditions, and some analytic conditions for…”
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Diffusion-limited aggregation on a tree by BARLOW, M. T, PEMANTLE, R, PERKINS, E. A

“…We study the following growth model on a regular d-ary tree. Points at distance n adjacent to the existing subtree are added with probabilities proportional to…”
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On the Filtration of Historical Brownian Motion by Barlow, Martin T., Perkins, Edwin A.

“…We show that the historical Brownian motion may be recovered from ordinary super-Brownian motion when the dimension d of the underlying Brownian motion is…”
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Some remarks on uniform boundary Harnack Principles by Barlow, Martin T, Karli, Deniz

“…We prove two versions of a boundary Harnack principle in which the constants do not depend on the domain…”
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The Liouville property and a conjecture of De Giorgi by Barlow, Martin T., Bass, Richard F., Gui, Changfeng

“…We consider bounded entire solutions of the nonlinear PDE Δu + u − u3 = 0 in ℝd and prove that under certain monotonicity conditions these solutions must be…”
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