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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Connection probabilities for random-cluster model and uniform spanning treeConnection probabilities for random-cluster model and uniform spanning tree
随机 聚类模型 均匀生成树 连接概率
2023/5/16
Conformal invariance of critical lattice models in two-dimensional has been vigorously studied for decades. The first example where the conformal invariance was rigorously verified was the planar unif...
Ising models on locally tree-like graphs
Ising model random sparse graphs cavity method Bethe measures belief propagation local weak convergence
2015/8/21
We consider Ising models on graphs that converge locally to trees. Examples include random regular graphs with bounded degree and uniformly random graphs with bounded average degree. We prove that the...
The weak limit of Ising models on locally tree-like graphs
Ising model the temperature the last beta sequence
2015/8/20
We consider the Ising model with inverse temperature β and without external field on sequences of graphs Gn which converge locally to the k-regular tree. We show that for such graphs the Ising m...
FACTOR MODELS ON LOCALLY TREE-LIKE GRAPHS
Factor models random graphs belief propagation Bethe measures Potts model independent set Gibbs measures free energy density local weak convergence
2015/8/20
We consider homogeneous factor models on uniformly sparse graph sequences converg-ing locally to a (unimodular) random tree T, and study the existence of the free energy density ,the limit of the log...
Semi-infinite paths of the 2d-Radial Spanning Tree
stochastic geometry random tree semi-infinite path asymptotic direction competition interface
2012/6/9
We study semi-infinite paths of the radial spanning tree (RST) of a Poisson point process in the plane. We first show that the expectation of the number of intersection points between semi-infinite pa...
Record process on the Continuum Random Tree
continuum random tree, records, cutting down a tree
2011/9/14
Abstract: We consider the number of cuts $X_n^*$ needed to isolate the root of the sub-tree spanned by $n$ leaves uniformly chosen at random in Aldous's continuum random tree $\ct$. We prove the almos...