6 citations · 8 across the 9 of their papers we have counts for
10 papers
Evolving fractal dimensions in iterative bicolored percolation
Shuo Wei, Haoyu Liu, Xin Sun +2
Criticality is traditionally regarded as an unstable, fine-tuned fixed point of the renormalization group. We introduce an iterative bicolored percolation process in two dimensions…
Liouville quantum gravity: from random planar maps to conformal field theory
Nina Holden, Xin Sun
Originating in theoretical physics, Liouville quantum gravity (LQG) has been an important topic in probability theory and mathematical physics in the past two decades. In this proc…
Analytic results in conformal field theory
Philine van Vliet, Emilio Trevisani, Ingo Runkel +4
Since the 1980s, many exact results have been discovered in CFT, from critical exponents to correlation functions to complete solutions of certain models. In , there is a…
Disconnection probability of Brownian motion on an annulus
Gefei Cai, Xuesong Fu, Xin Sun +1
We derive an exact formula for the probability that a Brownian path on an annulus does not disconnect the two boundary components of the annulus. The leading asymptotic behavior of…
The bulk one-arm exponent for the CLE percolations
Haoyu Liu, Xin Sun, Pu Yu +1
The conformal loop ensemble (CLE) is a conformally invariant random collection of loops. In the non-simple regime , it describes the scaling limit of the critical Fort…
Backbone exponent and annulus crossing probability for planar percolation
Pierre Nolin, Wei Qian, Xin Sun +1
We report the recent derivation of the backbone exponent for 2D percolation. In contrast to previously known exactly solved percolation exponents, the backbone exponent is a transc…
Annulus crossing formulae for critical planar percolation
Xin Sun, Shengjing Xu, Zijie Zhuang
We derive exact formulae for three basic annulus crossing events for the critical planar Bernoulli percolation in the continuum limit. The first is for the probability that there i…
Boundary touching probability and nested-path exponent for non-simple CLE
Morris Ang, Xin Sun, Pu Yu +1
The conformal loop ensemble (CLE) has two phases: for , the loops are simple and do not touch each other or the boundary; for , the loops are non-simple…
Bootstrap, Markov Chain Monte Carlo, and LP/SDP Hierarchy for the Lattice Ising Model
Minjae Cho, Xin Sun
Bootstrap is an idea that imposing consistency conditions on a physical system may lead to rigorous and nontrivial statements about its physical observables. In this work, we discu…
Backbone exponent for two-dimensional percolation
Pierre Nolin, Wei Qian, Xin Sun +1
We derive an exact expression for the celebrated backbone exponent for Bernoulli percolation in dimension two at criticality. It turns out to be a root of an elementary function. C…