2011/10/31 by Gesualdo Delfino, Jacopo Viti
Mathematics · Physics and Astronomy · #Cluster (spacecraft) #Combinatorics #Computer science #Critical exponent #Criticality #Geometry #Level crossing #Limit (mathematics) #Mathematical analysis #Mathematics #Percolation (cognitive psychology) #Percolation critical exponents #Percolation theory #Physics #Random Matrices and Applications #Rectangle #Scaling #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Topology (electrical circuits) #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1088/1751-8113/45/3/032005
published as J. Phys. A: Math. Theor. 45 (2012) 032005 · 13 pages, 5 figures. Published version with references, appendix and comparison with numerics added
arxiv created 2011/12/19 · openalex publication_date 2011/12/20 · arxiv updated 2014/10/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider two-dimensional percolation in the scaling limit close to criticality and use integrable field theory to obtain universal predictions for the probability that at least one cluster crosses between opposite sides of a rectangle of sides much larger than the correlation length and for the mean number of such crossing clusters.