Poisson suspensions and infinite ergodic theory
نویسندگان
چکیده
We investigate ergodic theory of Poisson suspensions. In the process, we establish close connections between finite and infinite measure preserving ergodic theory. Poisson suspensions thus provide a new approach to infinite measure ergodic theory. Fields investigated here are mixing properties, spectral theory, joinings. We also compare Poisson suspensions to the apparently similar looking Gaussian dynamical systems.
منابع مشابه
2 6 Fe b 20 08 POISSON SUSPENSIONS AND INFINITE ERGODIC THEORY
We investigate ergodic theory of Poisson suspensions. In the process, we establish close connections between finite and infinite measure preserving ergodic theory. Poisson suspensions thus provide a new approach to infinite measure ergodic theory. Fields investigated here are mixing properties, spectral theory, joinings. We also compare Poisson suspensions to the apparently similar looking Gaus...
متن کاملJa n 20 08 POISSON SUSPENSIONS AND INFINITE ERGODIC THEORY
We investigate ergodic theory of Poisson suspensions. In the process, we establish close connections between finite and infinite measure preserving ergodic theory. Poisson suspensions thus provide a new approach to infinite measure preserving ergodic theory. Fields investigated here are mixing properties, spectral theory, joinings. We also compare Poisson suspensions to the apparently similar l...
متن کاملErgodic Properties of an Infinite System of Particles Moving Independently in a Periodic Field*
We investigate the ergodic properties of a general class of infinite systems of independent particles which undergo nontrivial "collisions" with an external field, e.g. fixed convex barriers (the Lorentz gas). We relate the ergodic properties of these systems to the ergodic properties for a single particle moving in a finite box (with periodic boundary conditions) with the same dynamics. We pro...
متن کاملElectrostatic analysis of the charged surface in a solution via the finite element method: The Poisson-Boltzmann theory
Electrostatic potential as well as the local volume charge density are computed for a macromolecule by solving the Poisson-Boltzmann equation (PBE) using the finite element method (FEM). As a verification, our numerical results for a one dimensional PBE, which corresponds to an infinite-length macromolecule, are compared with the existing analytical solution and good agreement is found. As a ma...
متن کاملThe Shape Theorem for Route-lengths in Connected Spatial Networks on Random Points
For a connected network on Poisson points in the plane, consider the route-length D(r, θ) between a point near the origin and a point near polar coordinates (r, θ), and suppose ED(r, θ) = O(r) as r →∞. By analogy with the shape theorem for first-passage percolation, for a translation-invariant and ergodic network one expects r−1D(r, θ) to converge as r → ∞ to a constant ρ(θ). It turns out there...
متن کامل