The advantage of working with ‘n-succesful’ points is that the correlation between two such points, x, y , can be controlled using the treelike structure of circles centered at the two points.
A random walk proof of the Erdos-Taylor conjecture
We will see that there will also be another contribution to the entanglement entropy, coming from the residual singlets left straddling the endpoints after the treelike structures have been resolved.
Infinite Randomness Phases and Entanglement Entropy of the Disordered Golden Chain
This means the treelike structures form twice as fast as the singlets in the AFM phase.
Infinite Randomness Phases and Entanglement Entropy of the Disordered Golden Chain
Brownian motion on spatial trees: annealed law. ρ ◦ φ−1 and PS measurability of the laws PT 0 , and the convergence results of later sections, it will be useful to approximate the spaces T and S by treelike sets with only a ﬁnite number of branches.
Hausdorff measure of arcs and Brownian motion on Brownian spatial trees
Lyons, The Ising model and percolation on trees and treelike graphs, Comm.
Strong Spatial Mixing for Binary Markov Random Fields
Equivalently, K \G is treelike if it does not contain simple circuits of length greater than 2.
Random walks on random coset spaces with applications to Furstenberg entropy
First passage percolation on locally treelike networks. I. dense random graphs.
Flooding in Weighted Random Graphs
In fact, for all the graphs we consider, O(k ln n) steps is suﬃcient for our results. A typical graph also has most of its vertices treelike.
Viral Processes by Random Walks on Random Regular Graphs
Let G be a typical r-regular graph, and let v be a vertex of G, treelike to depth L1 = ⌊ǫ1 logr n⌋.
Viral Processes by Random Walks on Random Regular Graphs
The ideas of conducting the random walk to inﬁnity on a “treelike structure” of “not too slowly growing roads leading to inﬁnity” has been applied in [BZZ06].
A Stationary, Mixing and Perturbative Counterexample to the 0-1-law for Random Walk in Random Environment in Two Dimensions
The cavity method exploits the fact that the next shortest path connecting any two neighboring g-spins, after breaking the immediate path, is inﬁnite in the large system limit, and that instances where the cavity graph rooted in a g-spin are not locally treelike are statistically negligible.
Next nearest neighbour Ising models on random graphs
First passage percolation on locally treelike networks. I. dense random graphs.
Universality for first passage percolation on sparse random graphs
There is however no numerical evidences for the full treelike structure of states, as predicted by Parisi solution.
Some aspects of infinite range models of spin glasses: theory and numerical simulations
This approach is critical to the arguments used in where tree-like paths are approximated by with simpler treelike paths in 1-variation. (They would never converge in the ‘hyperbolic’ metric).
Some notes on trees and paths
If the data are the result of a simple treelike evolutionary process, we may model the process as a Markov chain.
Computational Tools for Evaluating Phylogenetic and Hierarchical Clustering Trees
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