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Sunday, July 26, 2020 | History

2 edition of Random walk on the incipient infinite cluster on trees found in the catalog.

Random walk on the incipient infinite cluster on trees

Martin T. Barlow

# Random walk on the incipient infinite cluster on trees

## by Martin T. Barlow

Written in English

Edition Notes

Classifications The Physical Object Statement by Martin T. Barlow and Takashi Kumagai. Series RIMS -- 1493 Contributions Kumagai, Takashi., Kyōto Daigaku. Sūri Kaiseki Kenkyūjo. LC Classifications MLCSJ 2008/00079 (Q) Pagination 30 p. ; Number of Pages 30 Open Library OL16508898M LC Control Number 2008558005

Random Walk on the Incipient Infinite Cluster for Oriented Percolation in High Dimensions Article (PDF Available) in Communications in Mathematical Physics (2) September with 40 Reads. Random walk on the incipient infinite cluster on trees. Illinois J. Math. 50 33–65 (electronic). Mathematical Reviews (MathSciNet): MR Zentralblatt MATH: Project Euclid:

Invasion percolation cluster, incipient inﬁnite cluster, r-point function, cluster size, simple random walk, Poisson point process. This is an electronic reprint of the original article published by the Institute of Mathematical Statistics in The Annals of Probability, , Vol. 36, No. 2, – Critical percolation clusters are believed to be ﬁnite in all dimensions, and it is rig-orously proved when d = 2 or d To avoid ﬁnite-size issues associated with random walk on a ﬁnite cluster, it is convenient to consider random walk on the incipient inﬁnite.

Download PDF: Sorry, we are unable to provide the full text but you may find it at the following location(s): (external link).   Part of the Lecture Notes in Mathematics book series (LNM, volume G. Slade, Random walk on the incipient infinite cluster for oriented percolation in high dimensions. Commun. Math. Phys. , – () CrossRef zbMATH Google Scholar. M.T. Barlow, T. Kumagai, Random walk on the incipient infinite cluster on trees. Illinois J.

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### Random walk on the incipient infinite cluster on trees by Martin T. Barlow Download PDF EPUB FB2

Random Walk on The Incipient Infinite Cluster on Trees Article (PDF Available) in Illinois journal of mathematics 50() April with 47 Reads How we measure 'reads'.

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract. Let G be the incipient infinite cluster (IIC) for percolation on a homogeneous tree of degree n0 + 1. We obtain estimates for the transition density of the the continuous time simple random walk Y on G; the process satisfies anomalous diffusion and has spectral dimension 4.

Random walk on the incipient inﬁnite cluster on trees Martin T. Barlow1, Takashi Kumagai2 Abstract. Let G be the incipient inﬁnite cluster (IIC) for percolation on a homogeneous tree of degree n0 +1.

We obtain estimates for the transition density of the the continuous. Abstract. We consider simple random walk on the incipient infinite cluster for the spread-out model of oriented percolation on Zd × Z+. In dimensions d> 6, we obtain bounds on exit times, transition probabilities, and the range of the random walk, which establish that the spectral dimension of the incipient infinite cluster is 43, and thereby prove a version of the Alexander– Orbach.

We consider simple random walk on the incipient infinite cluster for the spread-out model of oriented percolation on $${\mathbb{Z}}^{d} \times {\mathbb{Z}}_+$$.

In dimensions d > 6, we obtain bounds on exit times, transition probabilities, and the range of the random walk, which establish that the spectral dimension of the incipient infinite cluster is $$\frac {4}{3}$$, and thereby prove a Cited by: Return Probabilities of a Simple Random Walk on Percolation Clusters Heicklen, Deborah and Hoffman, Christopher, Electronic Journal of Probability, ; Critical percolation and the incipient infinite cluster on Galton-Watson trees Michelen, Marcus, Electronic Communications in Probability, Books.

An illustration of two cells of a film strip. Video. An illustration of an audio speaker. Audio. An illustration of a " floppy disk. Random walk on the incipient infinite cluster for oriented percolation in high dimensions Item Preview remove-circle Share or Embed This Item.

The incipient infinite cluster of the uniform infinite half-planar triangulation Richier, Loïc, Electronic Journal of Probability, Central limit theorem for biased random walk on multi-type Galton-Watson trees Dembo, Amir and Sun, Nike, Electronic Journal of Probability, Random walk on the incipient infinite cluster on trees.

Illinois J. Math. 50 () 33– Mathematical Reviews (MathSciNet): MR Zentralblatt MATH: Project Euclid: CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We consider invasion percolation on a rooted regular tree.

For the infinite cluster invaded from the root, we identify the scaling behaviour of its r-point function for any r ≥ 2 and of its volume both at a given height and below a given height. In addition, we derive scaling estimates for simple random walk on the. BibTeX @ARTICLE{Barlow_randomwalk, author = {Martin T.

Barlow and Antal A. Járai and Takashi Kumagai and Gordon Slade}, title = {Random walk on the incipient infinite cluster on trees}, journal = {Illinois J.

Math. (Doob}, year = {}}. adshelp[at] The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A. [5] Barlow, M. and Kumagai, T. () Random walk on the incipient infinite cluster on trees.

Illinois J. Math. 50 33 – [6] Benjamini, I. and Schramm, O. () Recurrence of distributional limits of finite planar graphs. We study the asymptotic behavior the exit times of random walk from Euclidean balls around the origin of the incipient infinite cluster in a manner inspired by.

'This book, written with great care, is a comprehensive course on random walks on graphs, with a focus on the relation between rough geometric properties of the underlying graph and the asymptotic behavior of the random walk on it. It is accessible to graduate students but.

We study the simple random walk on the uniform spanning tree on $${\mathbb {Z}^2}$$.We obtain estimates for the transition probabilities of the random walk, the distance of the walk from its starting point after n steps, and exit times of both Euclidean balls and balls in the intrinsic graph metric.

In particular, we prove that the spectral dimension of the uniform spanning tree on \({\mathbb. Thus, somewhat surprisingly, the two clusters behave differently; in fact, we prove that their laws are mutually singular. In addition, we derive scaling estimates for simple random walk on the cluster starting from the root.

We show that the invasion percolation cluster is stochastically dominated by the incipient infinite cluster. The first part of the paper is devoted to proving an almost sure analog of H. Kesten's subdiffusivity theorem for the random walk on the incipient infinite cluster and the invasion percolation.

Abstract: The uniform measure on the set of all spanning trees of a finite graph is a classical object Read More. July 7, Abstract: We show that random walk on the incipient infinite cluster (IIC) of two-dimensional critical percolation is subdiffusive in Read More.

Abstract. Abstract. Let G be the incipient infinite cluster (IIC) for percolation on a homogeneous tree of degree n0 + 1. We obtain estimates for the transition density of the the continuous time simple random walk Y on G; the process satisfies anomalous diffusion and has spectral dimension.

Random walk on the incipient infinite cluster on trees. Illinois J. Math. 50 (), no.(electronic). Zentralblatt MATH: Project Euclid: Looptrees have recently arisen in the study of critical percolation on the uniform infinite planar triangulation.

Here we consider random infinite looptrees defined as the local limit of the looptree associated with a critical Galton–Watson tree conditioned to be large. We study simple random walk on these infinite looptrees by means of providing estimates on volume and resistance growth.Random walks on Galton-Watson trees with infinite variance offspring distribution conditioned to survive.

Random walk on the incipient inﬁnite cluster for oriented percolation in high dimensions, (). Random walk on the incipient inﬁnite cluster on trees.