Related papers: Young Towers for Product Systems
Recurrence plots exhibit line structures which represent typical behaviour of the investigated system. The local slope of these line structures is connected with a specific transformation of the time scales of different segments of the…
Parametrized measures (or Young measures) enable to reformulate non-convex variational problems as convex problems at the cost of enlarging the search space from space of functions to space of measures. To benefit from such machinery, we…
We obtain scaling and local limit results for large random Young tableaux of fixed shape $\lambda^0$ via the asymptotic analysis of a determinantal point process due to Gorin and Rahman (2019). More precisely, we prove: (1) an explicit…
This paper shows that for certain local topological properties, given a locally quasi-finite, flat and locally finitely presented map of schemes $f\colon X\to Y$, if $Y$ has the property, then so does $X$. We also show that being locally…
For geometric Lorenz attractors (including the classical Lorenz attractor) we obtain a greatly simplified proof of the central limit theorem which applies also to the more general class of codimension two singular hyperbolic attractors. We…
We use Wagner's algorithm to estimate the number of periodic points of certain selfmaps on compact surfaces with boundary. When counting according to homotopy classes, we can use the asymptotic density to measure the size of sets of…
We characterize Young measures generated by gradients of bi-Lipschitz orientation-preserving maps in the plane. This question is motivated by variational problems in nonlinear elasticity where the orientation preservation and injectivity of…
A major line of questions in quantum information and computing asks how quickly locally random circuits converge to resemble global randomness. In particular, approximate k-designs are random unitary ensembles that resemble random circuits…
Irreversible Port Hamiltonian Systems are departure of Port Hamiltonian Systems as they are generated not only by a Hamiltonian function but also by an entropy function and defined with respect to a quasi-Poisson bracket which embeds the…
Renewal theorems are developed for point processes with interarrival times $W_n=\xi(X_{n+1}X_n\cdots)$, where $(X_n)_{n\in\mathbb Z}$ is a stochastic process with finite state space $\Sigma$ and $\xi\colon\Sigma_A\to\mathbb R$ is a H\"older…
When a biological system robustly corrects component-level errors, the direct pressure on component performance declines. Components may become less reliable, maintain more genetic variability, or drift neutrally in design, creating the…
We give geometric conditions that are necessary and sufficient for the existence of Sinai-Ruelle-Bowen (SRB) measures for $C^{1+\alpha}$ surface diffeomorphisms, thus proving a version of the Viana conjecture. As part of our argument we…
The decay of a general time dependent structure factors is considered. The dynamics is that of stochastic field equations of the Langevin type, where the systematic generalized force is a functional derivative of some classical field…
For non uniformly hyperbolic maps of the interval with exponential decay of correlations we prove that the law of closest return to a given point when suitably normalized is almost surely asymptotically exponential. A similar result holds…
As it was argued by Anderson [Science 177, 393 (1972)], the "reductionist" hypothesis does not by any means imply a "constructionist" one. Hence, in general, the behavior of large and complex aggregates of elementary components can not be…
We consider families of fast-slow skew product maps of the form \begin{align*} x_{n+1} = x_n+\epsilon a(x_n,y_n,\epsilon), \quad y_{n+1} = T_\epsilon y_n, \end{align*} where $T_\epsilon$ is a family of nonuniformly expanding maps, and prove…
Let $X^{(2)}$ denote the second symmetric product space of a partially ordered vector space $X$, endowed with the projective cone. A characterization of linear maps $T\colon X^{(2)}\to X^{(2)}$ which preserve the set of all positive…
For a class of linear switched systems in continuous time a controllability condition implies that state feedbacks allow to achieve almost sure stabilization with arbitrary exponential decay rates. This is based on the Multiplicative…
We investigate the structure of return-time sets determined by orbits along polynomial tuples in minimal topological dynamical systems. Building on the topological characteristic factor theory of Glasner, Huang, Shao, Weiss, and Ye, we…
Many complex engineering systems consist of multiple subsystems that are developed by different teams of engineers. To analyse, simulate and control such complex systems, accurate yet computationally efficient models are required. Modular…