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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Percolation in Strongly Correlated Systems: The Massless Gaussian Field
强相关系统 渗透 无质量 高斯场
2023/5/5
In this talk, we will show several results for correlated nearest neighbor site percolation on Z^d. In particular, we will show that in three dimensions the strongly correlated massless harmonic cryst...
Directed random walk on an oriented percolation cluster
Random walk, dynamical random environment, oriented percolation, supercritical cluster, central limit theorem in random environment
2012/4/16
We consider directed random walk on the infinite percolation cluster generated by supercritical oriented percolation, or equivalently the space-time embedding of the `ancestral lineage' of an individu...
Bond percolation on isoradial graphs
Bond percolation isoradial graph rhombic tiling Penrose tiling inhomogeneous percolation universality
2012/4/18
In an investigation of percolation on isoradial graphs, we prove the criticality of canonical bond percolation on isoradial embeddings of planar graphs, thus extending celebrated earlier results for h...
Homogenization and continuum percolation
Homogenization random media continuum percolation
2011/9/22
Abstract: We propose continuum percolation theory to study homogenization problems of elliptic equations.Our aim is to improve and extend similar results that have been obtained for periodic domains u...
Abstract: Secrecy graphs model the connectivity of wireless networks under secrecy constraints. Directed edges in the graph are present whenever a node can talk to another node securely in the presenc...
The asymptotic shape, large deviations and dynamical stability in first-passage percolation on cones
The asymptotic shape dynamical stability cones Probability
2011/9/2
Abstract: In this paper we consider first-passage percolation on certain subgraphs of the $\Z^d$ nearest neighbour graph. We present a three-fold extension of the Shape Theorem. Firstly, we show that ...
Asymptotics of first-passage percolation on 1-dimensional graphs
Asymptotics of first-passage percolation 1-dimensional graphs Probability
2011/9/2
Abstract: In this paper we consider standard first-passage percolation on certain 1-dimensional periodic graphs. One such graph of particular interest is the $\Z\times\{0,1,...,K-1\}^{d-1}$ nearest ne...
Linear algebra and bootstrap percolation
Bootstrap percolation linear algebra weak saturation
2011/8/29
Abstract: In $\HH$-bootstrap percolation, a set $A \subset [n]$ of initially `infected' vertices spreads by infecting vertices which are the only uninfected vertex in an edge of the hypergraph $\HH \s...
Abstract: Graph bootstrap percolation is a deterministic cellular automaton which was introduced by Bollob\'as in 1968, and is defined as follows. Given a graph $H$, and a set $G \subset E(K_n)$ of in...
Planar percolation with a glimpse of Schramm-Loewner Evolution
Planar percolation Schramm-Loewner Evolution Statistical Mechanics
2011/8/22
Abstract: In recent years, important progress has been made in the field of two-dimensional statistical physics. One of the most striking achievement is probably the proof of conformal invariance of p...
Heterogeneous-k-core versus Bootstrap Percolation on Complex Networks
Heterogeneous-k-core Bootstrap Percolation Complex Networks
2011/3/3
We introduce the heterogeneous-k-core, which generalizes the k-core, and contrast it with bootstrap percolation.
On the speed of biased random walk in translation invariant percolation
speed of biased random translation invariant percolation
2011/2/21
For biased random walk on the infinite cluster in supercritical i.i.d.percolation on Z2, where the bias of the walk is quantified by a parameter > 1,it has been conjectured (and partly proved) that ...
Bootstrap percolation on the random graph G_{n,p}
Bootstrap percolation random graph G_{n,p}
2011/2/21
Bootstrap percolation on the random graph Gn,p is a process of spread of “activation” on a
given realization of the graph with a given number of initially active nodes. At each step those vertices wh...
Poincaré inequality for Markov random fields via disagreement percolation
Poincar´ e inequality weak Poincar´ e inequality Gibbs mea-
2011/1/20
We consider Markov random fields of discrete spins on the lattice Zd. We use a technique of coupling of conditional distributions. If under the coupling the disagreement cluster is “sufficiently” subc...
Uniform approximation of the integrated density of states for long-range percolation Hamiltonians
the integrated density of states long-range percolation Hamiltonians
2010/11/23
In this paper we study the spectrum of long-range percolation graphs. The underlying geometry is given in terms of a finitely generated amenable group. We prove that the integrated density of states (...