Related papers: Metastability in the Furstenberg-Zimmer tower

Unlike the ferropnictide superconductors, which crystallize in a tetragonal crystal structure, binary FeAs forms in an orthorhombic crystal structure, where the local atomic environment resembles a highly distorted variant of the FeAs4…

The derivation of the state of the art tensorial versions of Fundamental Measure Theory (a form of classical Density Functional Theory for hard spheres) are re-examined in the light of the recently introduced concept of global stability of…

Let $\theta$ be a finitely supported probability measure on $\mathrm{SL}(2,\mathbb{C})$, and suppose that the semigroup generated by $\mathcal{G}:=\mathrm{supp}(\theta)$ is strongly irreducible and proximal. Let $\mu$ denote the Furstenberg…

We consider a fully polarized ultracold Fermi gas interacting through a p-wave Feshbach resonance. Using a two-channel model, we find the effective potential at the point where the p-wave scattering length goes to zero. Here the effective…

Hyperuniformity is a property of certain heteroneous media in which density fluctuations in the long wavelength range decay to zero. In reciprocal space this behavior translates into a decay of Fourier intensities in the range near small…

We give a self-contained treatment of the theory of persistence modules indexed over the real line. We give new proofs of the standard results. Persistence diagrams are constructed using measure theory. Linear algebra lemmas are simplified…

Using an infinitary version of the Hypergraph Removal Lemma due to Towsner, we prove a model-theoretic higher amalgamation result. In particular, we obtain an independent amalgamation property which holds in structures which are measurable…

Sinai proved that a nonatomic ergodic measure-preserving system has any Bernoulli shift of no greater entropy as a factor. Given a Bernoulli shift, we show that any other Bernoulli shift that is of strictly less entropy and is…

The higher-order superintegrability of systems separable in polar coordinates is studied using an approch that was previously applied for the study of the superintegrability of a generalized Smorodinsky-Winternitz system. The idea is that…

We consider random walks on semisimple Lie groups where the support of the step distribution generates (as a group) a Zariski dense discrete subgroup of infinite covolume. When the semisimple Lie group has property (T), we show that the…

Series of extended Epstein type provide examples of non-trivial zeta functions with important physical applications. The regular part of their analytic continuation is seen to be a convergent or an asymptotic series. Their singularity…

The general fluctuation theory is reviewed with special attention to the role played by different ensembles, and is extended to incorporate stationary metastable states obtained in the long time limit. The fluctuation in a quantity depends…

Shortly after Szemer\'edi's proof that a set of positive upper density contains arbitrarily long arithmetic progressions, Furstenberg gave a new proof of this theorem using ergodic theory. This gave rise to the field of ergodic Ramsey…

We study Tao's finitary viewpoint of convergence in metric spaces, as captured by the notion of metastability. We adopt the perspective of continuous model theory. We show that, in essence, metastable convergence with a given rate is the…

We introduce two properties: strong R-property and $C(q)$-property, describing a special way of divergence of nearby trajectories for an abstract measure preserving system. We show that systems satisfying the strong R-property are disjoint…

We prove an inverse of Furstenberg's correspondence principle stating that for all measure preserving systems $(X,\mu,T)$ and $A\subset X$ measurable there exists a set $E \subset \mathbb{N}$ such that \[ \mu\left( \bigcap_{i=1}^k…

In this paper, some characterizations about transitivity, mildly mixing property, $\mathbf{a}$-transitivity, equicontinuity, uniform rigidity and proximality of Zadeh's extensions restricted on some invariant closed subsets of the space of…

Magnetic permeabilities derived for infinite, periodic media are used in the Fresnel equation to calculate the reflection from corresponding semi-infinite media. By comparison to finite-difference-time-domain (FDTD) simulations, we find…

Very recently, Green and Sawhney obtained a quasipolynomial bound in the Furstenberg--S\'ark\"ozy theorem for square differences by proving an ''arithmetic level-$d$'' inequality, thereby yielding a greatly improved density increment…

In a recent comment, M. Kosterlitz described how the discrepancy about the lack of broken translational symmetry in two dimensions - doubting the existence of 2D crystals - and the first computer simulations foretelling 2D crystals at least…