5 papers
Higher-order hyperuniformity of random measures
Michael Björklund
We study higher-order hyperuniformity through the large-scale variance of local -point patterns, and write $\HU_k$ for the resulting condition; $\HU_1$ is ordinary hyperuniformi…
Completely Positive Entropy and Fourier Central Limit Theorems for Stationary Random Measures
Michael Björklund
We prove an almost-everywhere Fourier central limit theorem for stationary random measures on $\bR^d$ with local second moments whose translation action is essentially free and has…
Hyperuniform Delone Realizations and Rigidity
Michael Björklund
We prove a measurable realization theorem for hyperuniform Delone point processes. In dimensions \(d\geq2\), for every prescribed \(q\geq1\), every essentially free ergodic p.m.p.\…
Stealthy point processes and lattice induction
Michael Björklund
We prove a realization theorem for stealthy point processes based on lattice induction, together with a converse in dimension one. Every probability-preserving -action…
Hyperuniformity of random measures on Euclidean and hyperbolic spaces
Michael Björklund, Mattias Byléhn
We investigate lower asymptotic bounds of number variances for invariant locally square-integrable random measures on Euclidean and real hyperbolic spaces. In the Euclidean case we…