2014
DOI: 10.1038/srep05495
|View full text |Cite
|
Sign up to set email alerts
|

Shortest path and Schramm-Loewner Evolution

Abstract: We numerically show that the statistical properties of the shortest path on critical percolation clusters are consistent with the ones predicted for Schramm-Loewner evolution (SLE) curves for κ = 1.04 ± 0.02. The shortest path results from a global optimization process. To identify it, one needs to explore an entire area. Establishing a relation with SLE permits to generate curves statistically equivalent to the shortest path from a Brownian motion. We numerically analyze the winding angle, the left passage pr… Show more

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1

Citation Types

0
16
0

Year Published

2015
2015
2024
2024

Publication Types

Select...
5
2

Relationship

0
7

Authors

Journals

citations
Cited by 22 publications
(16 citation statements)
references
References 80 publications
0
16
0
Order By: Relevance
“…To identify and analyse the CP structure we use the t -core decomposition, as proposed in (ref. 4 ). Similar to the k -core decomposition 17 , this method progressively prunes a network by recursively removing nodes that are part of the least number of triangles.…”
Section: Resultsmentioning
confidence: 99%
See 3 more Smart Citations
“…To identify and analyse the CP structure we use the t -core decomposition, as proposed in (ref. 4 ). Similar to the k -core decomposition 17 , this method progressively prunes a network by recursively removing nodes that are part of the least number of triangles.…”
Section: Resultsmentioning
confidence: 99%
“…The network undergoes a transition from a state where the size of the core is comparable to the system size but is of small coreness to a state with a small core and relatively large coreness. Since the empirical WAN is known to have a small core size of ∼2.3% but high inter-connectivity within the core 4 , it should be found in regime B with l min < θ ≤ l max , where the value of λ is largest (see Fig. 4 ).…”
Section: Resultsmentioning
confidence: 99%
See 2 more Smart Citations
“…the shortest paths on critical percolation clusters with κ = 1.04±0.02 [100], are examples of unusual universality classes. Watersheds can also be defined in higher dimensions [117].…”
Section: Introductionmentioning
confidence: 99%