P Gonçalves,M Jara,R Marinho et al.
P Gonçalves et al.
We study the scaling properties of the non-equilibrium stationary states (NESS) of a reaction-diffusion model. Under a suitable smallness condition, we show that the density of particles satisfies a law of large numbers with respect to the ...
Global well-posedness of the 2D nonlinear Schrödinger equation with multiplicative spatial white noise on the full space [0.03%]
带有乘性空间白噪声的二维非线性薛定谔方程在整个空间上的整体适定性问题
Arnaud Debussche,Ruoyuan Liu,Nikolay Tzvetkov et al.
Arnaud Debussche et al.
We consider the nonlinear Schrödinger equation with multiplicative spatial white noise and an arbitrary polynomial nonlinearity on the two-dimensional full space domain. We prove global well-posedness by using a gauge-transform introduced ...
March Boedihardjo,Thomas Strohmer,Roman Vershynin
March Boedihardjo
Differential privacy is a mathematical concept that provides an information-theoretic security guarantee. While differential privacy has emerged as a de facto standard for guaranteeing privacy in data sharing, the known mechanisms to achiev...
Harnack inequality and one-endedness of UST on reversible random graphs [0.03%]
可逆随机图上的UST的Harnack不等式和一端性
Nathanaël Berestycki,Diederik van Engelenburg
Nathanaël Berestycki
We prove that for recurrent, reversible graphs, the following conditions are equivalent: (a) existence and uniqueness of the potential kernel, (b) existence and uniqueness of harmonic measure from infinity, (c) a new anchored Harnack inequa...
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...