An asymptotic formula for the variance of the number of zeroes of a stationary Gaussian process [0.03%]
零点个数方差的渐近公式
Eran Assaf,Jeremiah Buckley,Naomi Feldheim
Eran Assaf
We study the variance of the number of zeroes of a stationary Gaussian process on a long interval. We give a simple asymptotic description under mild mixing conditions. This allows us to characterise minimal and maximal growth. We show that...
Biased [Formula: see text] periodic Aztec diamond and an elliptic curve [0.03%]
带有偏置的[公式见正文中文章]周期阿兹赖钻石和椭圆曲线
Alexei Borodin,Maurice Duits
Alexei Borodin
We study random domino tilings of the Aztec diamond with a biased 2×2 periodic weight function and associate a linear flow on an elliptic curve to this model. Our main result is a double integral formula for the correlation kernel, in ...
Jonas Arista,Elia Bisi,Neil O&#x;Connell
Jonas Arista
We study a discrete-time Markov process on triangular arrays of matrices of size d≥1, driven by inverse Wishart random matrices. The components of the right edge evolve as multiplicative random walks on positive definite matrices with...
Nathanaël Berestycki,Marcin Lis,Wei Qian
Nathanaël Berestycki
We study the dimer model on subgraphs of the square lattice in which vertices on a prescribed part of the boundary (the free boundary) are possibly unmatched. Each such unmatched vertex is called a monomer and contributes a fixed multiplica...
Péter Bálint,Henk Bruin,Dalia Terhesiu
Péter Bálint
We prove limit laws for infinite horizon planar periodic Lorentz gases when, as time n tends to infinity, the scatterer size ρ may also tend to zero simultaneously at a sufficiently slow pace. In particular we obtain a non-standard Cen...
Global solutions of aggregation equations and other flows with random diffusion [0.03%]
具随机扩散的聚集方程等流的全局解
Matthew Rosenzweig,Gigliola Staffilani
Matthew Rosenzweig
Aggregation equations, such as the parabolic-elliptic Patlak-Keller-Segel model, are known to have an optimal threshold for global existence versus finite-time blow-up. In particular, if the diffusion is absent, then all smooth solutions wi...
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...