Related papers: Almost Countable Spectrum and Logarithmic Sarnak C…
We work in set-theory without choice ZF. Denoting by AC(N) the countable axiom of choice, we show in ZF+AC(N) that the closed unit ball of a uniformly convex Banach space is compact in the convex topology (an alternative to the weak…
In this paper, we develop tools to establish almost sure stability of stochastic switched systems whose switching signal is constrained by an automaton. After having provided the necessary generalizations of existing results in the setting…
We present a streamlined proof of a result essentially present in previous work of the author, namely that for every set $S = \{s_1, s_2, \ldots\} \subset \mathbb{N}$ of zero Banach density and finite set $A$, there exists a minimal…
A countable, bounded degree graph is almost finite if it has a tiling with isomorphic copies of finitely many F\o lner sets, and we call it strongly almost finite, if the tiling can be randomized so that the probability that a vertex is on…
Entropy rate is a real valued functional on the space of discrete random sources which lacks a closed formula even for subclasses of sources which have intuitive parameterizations. A good way to overcome this problem is to examine its…
We generalize the notions of the St\"ackel transform and the coupling constant metamorphosis to quasi-exactly solvable systems. We discover that for a variety of one-dimensional and separable multidimensional quasi-exactly solvable systems,…
Almost sure reachability refers to the property of a stochastic system whereby, from any initial condition, the system state reaches a given target set with probability one. In this paper, we study the problem of certifying almost sure…
Recently Kazakov, Vieira and the author conjectured the Y-system set of equations describing the planar spectrum of AdS/CFT. In this paper we solve the Y-system equations in the strong coupling scaling limit. We show that the…
We introduce the property of having good subgroups for actions of countable discrete groups on compact metrizable spaces, and show that it implies comparison when the acting group is amenable. As a consequence, free actions on…
We are interested in dendrites for which all invariant measures of zero-entropy mappings have discrete spectrum, and we prove that this holds when the closure of the endpoint set of the dendrite is countable. This solves an open question…
Coalgebras in a Kleisli category yield a generic definition of trace semantics for various types of labelled transition systems. In this paper we apply this generic theory to generative probabilistic transition systems, short PTS, with…
Contraction rates of time-varying maps induced by dynamical systems illuminate a wide range of asymptotic properties with applications in stability analysis and control theory. In finite-dimensional smoothly varying inner-product spaces…
We prove a log average almost-sure invariance principle (log asip) for renewal processes with positive i.i.d. gaps in the domain of attraction of an $\alpha$-stable law with $0<\alpha<1$. Dynamically, this means that renewal and…
We prove the Almost Sure Invariance Principle (ASIP) with close to optimal error rates for nonuniformly hyperbolic maps. We do not assume exponential contraction along stable leaves, therefore our result covers in particular slowly mixing…
We show that the typical dynamical system sometimes begins to behave like a non-deterministic system with a small classical entropy, and this behavior lasts an extremely long time, until the system starts decreasing entropy. Then again it…
Countable $\mathcal{L}$-structures $\mathcal{N}$ whose isomorphism class supports a permutation invariant probability measure in the logic action have been characterized by Ackerman-Freer-Patel to be precisely those $\mathcal{N}$ which have…
The Kotani-Last conjecture states that every ergodic operator in one space dimension with non-empty absolutely continuous spectrum must have almost periodic coefficients. This statement makes sense in a variety of settings; for example,…
We prove that topologically generic orbits of C0 transitive and non-uniquely ergodic dynamical systems, exhibit an extremely oscillating asymptotical statistics. Precisely, the minimum weak* compact set of invariant probabilities, that…
We report the theoretical discovery of a large class of 2D tight-binding models containing nearly-flat bands with nonzero Chern numbers. In contrast with previous studies, where nonlocal hoppings are usually required, the Hamiltonians of…
The absolute sets of local systems on a smooth complex algebraic variety are the subject of a conjecture of N. Budur and B. Wang based on an analogy with special subvarieties of Shimura varieties. An absolute set should be the…