Juhan Aru,Antoine Jego,Janne Junnila
Juhan Aru
We consider the imaginary Gaussian multiplicative chaos, i.e. the complex Wick exponential μ β : = : e i β Γ ( x ) : for a log-correlated Gaussian field Γ in d ≥ 1 dimensions. We prove a basic density resu...
Random walks on hyperbolic spaces: Concentration inequalities and probabilistic Tits alternative [0.03%]
双曲空间上的随机游走：集中不等式和概率Tits替代定理
Richard Aoun,Cagri Sert
Richard Aoun
The goal of this article is two-fold: in a first part, we prove Azuma-Hoeffding type concentration inequalities around the drift for the displacement of non-elementary random walks on hyperbolic spaces. For a proper hyperbolic space M, we o...
Approximation of martingale couplings on the line in the adapted weak topology [0.03%]
有适应性的弱拓扑下关于实直线上的鞅耦合的逼近问题
M Beiglböck,B Jourdain,W Margheriti et al.
M Beiglböck et al.
Our main result is to establish stability of martingale couplings: suppose that π is a martingale coupling with marginals μ , ν . Then, given approximating marginal measures μ ~ ≈ μ , ν ~ ≈ ν...
Anna Erschler,Tianyi Zheng
Anna Erschler
We prove the law of large numbers for the drift of random walks on the two-dimensional lamplighter group, under the assumption that the random walk has finite ( 2 + ϵ ) -moment. This result is in contrast with classical examples of a...
Adam W Marcus,Daniel A Spielman,Nikhil Srivastava
Adam W Marcus
We study three convolutions of polynomials in the context of free probability theory. We prove that these convolutions can be written as the expected characteristic polynomials of sums and products of unitarily invariant random matrices. Th...
Oleg Butkovsky,Konstantinos Dareiotis,Máté Gerencsér
Oleg Butkovsky
We give a new take on the error analysis of approximations of stochastic differential equations (SDEs), utilizing and developing the stochastic sewing lemma of Lê (Electron J Probab 25:55, 2020. 10.1214/20-EJP442). This approach allows one...
Non-simple conformal loop ensembles on Liouville quantum gravity and the law of CLE percolation interfaces [0.03%]
Liouville量子重力上的非简单共形环系及CLE渗流界面的规律
Jason Miller,Scott Sheffield,Wendelin Werner
Jason Miller
We study the structure of the Liouville quantum gravity (LQG) surfaces that are cut out as one explores a conformal loop-ensemble CLE κ ' for κ ' in (4, 8) that is drawn on an independent γ -LQG surface for γ 2 = 16 ...
Hugo Duminil-Copin,Ioan Manolescu,Vincent Tassion
Hugo Duminil-Copin
This paper is studying the critical regime of the planar random-cluster model on Z 2 with cluster-weight q ∈ [ 1 , 4 ) . More precisely, we prove crossing estimates in quads which are uniform in their boundary conditions and depend...
Omer Angel,Tom Hutchcroft,Antal Járai
Omer Angel
Consider a critical branching random walk on Z d , d ≥ 1 , started with a single particle at the origin, and let L(x) be the total number of particles that ever visit a vertex x. We study the tail of L(x) under suitable conditions o...
Yukun He,Antti Knowles
Yukun He
We consider a class of sparse random matrices which includes the adjacency matrix of the Erdős-Rényi graph G ( N , p ) . We show that if N ε ⩽ N p ⩽ N 1 / 3 - ε then all nontrivial eigenvalues away from 0 have...