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...
Regularity of SLE in [Formula: see text] and refined GRR estimates [0.03%]
SLE在[公式请参见文本]中的正则性及GRR估计的改进
Peter K Friz,Huy Tran,Yizheng Yuan
Peter K Friz
Schramm-Loewner evolution ( SLE κ ) is classically studied via Loewner evolution with half-plane capacity parametrization, driven by κ times Brownian motion. This yields a (half-plane) valued random field γ = γ ( t , &...
Joseph Najnudel,Bálint Virág
Joseph Najnudel
The bead process introduced by Boutillier is a countable interlacing of the Sine 2 point processes. We construct the bead process for general Sine β processes as an infinite dimensional Markov chain whose transition mechanism is expl...
Giorgio Cipolloni,László Erdős,Dominik Schröder
Giorgio Cipolloni
We consider large non-Hermitian real or complex random matrices X with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the...
Ilya Chevyrev,Peter K Friz,Alexey Korepanov et al.
Ilya Chevyrev et al.
We consider deterministic fast-slow dynamical systems on R m × Y of the form x k + 1 ( n ) = x k ( n ) + n - 1 a ( x k ( n ) ) + n - 1 / α b ( x k ( n ) ) v ( y k ) , y k + 1 = f ( y k ) , where &...