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Central limit theorems (CLTs) have a long history in probability and statistics. They play a fundamental role in constructing valid statistical inference procedures. Over the last century, various techniques have been developed in…
We obtain a Central Limit Theorem for closed Riemannian manifolds, clarifying along the way the geometric meaning of some of the hypotheses in Bhattacharya and Lin's Omnibus Central Limit Theorem for Fr\'echet means. We obtain our CLT…
Gouezel and Sarig introduced operator renewal theory as a method to prove sharp results on polynomial decay of correlations for certain classes of nonuniformly expanding maps. In this paper, we apply the method to planar dispersing…
We prove central limit theorems (CLTs) for topological functionals of Bernoulli bond percolation on infinite graphs beyond the Euclidean lattice $\mathbb{Z}^{d}$. For quasi-transitive graphs of subexponential growth, we show that the number…
Discrete systems with long-range interactions are considered. Continuous medium models as continuous limit of discrete chain system are defined. Long-range interactions of chain elements that give the fractional equations for the medium…
We study the Feynman graph structure and compute certain exact four-point correlation functions in chiral CFT$_4$ proposed by \"{O}.G\"{u}rdo\u{g}an and one of the authors as a double scaling limit of $\gamma$-deformed $\mathcal{N}=4$ SYM…
In his 1996 paper, Talagrand highlighted that the Law of Large Numbers (LLN) for independent random variables can be viewed as a geometric property of multidimensional product spaces. This phenomenon is known as the concentration of…
We calculate the exact values of the holomorphic observables of {\cal N}=4 supersymmetric SU(N) Yang-Mills theory deformed by mass terms which preserve {\cal N}=1 SUSY. These include the chiral condensates in each massive vacuum of the…
Pointwise minimum norm control laws for hybrid dynamical systems are proposed. Hybrid systems are given by differential equations capturing the continuous dynamics or flows, and by difference equations capturing the discrete dynamics or…
We consider families of random products of close-by Anosov diffeomorphisms, and show that statistical stability and linear response hold for the associated families of equivariant and stationary measures. Our analysis rely on the study of…
A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are…
In this article we study networks of coupled dynamical systems with time-delayed connections. If two such networks hold different delays on the connections it is in general possible that they exhibit different dynamical behavior as well. We…
A Central Limit Theorem is proved for linear random fields when sums are taken over finite disjoint union of rectangles. The approach does not rely upon the use of Beveridge Nelson decomposition and the conditions needed are similar to…
We consider multimodal C^3 interval maps f satisfying a summability condition on the derivatives D_n along the critical orbits which implies the existence of an absolutely continuous f -invariant probability measure mu. If f is…
A comparison of escape rates from one and from two holes in an experimental container (e.g. a laser trap) can be used to obtain information about the dynamics inside the container. If this dynamics is simple enough one can hope to obtain…
Using proof-theoretic methods in the style of proof mining, we give novel computationally effective limit theorems for the convergence of the Cesaro-means of certain sequences of random variables. These results are intimately related to…
By extending methods of arXiv:1503.01409, we investigate the bound on the growth of higher point OTOCs by studying their complex analytical properties. We explore some subtleties in our mathematical investigation, and carefully examine the…
In order to obtain functional limit theorems for heavy tailed stationary processes arising from dynamical systems, one needs to understand the clustering patterns of the tail observations of the process. These patterns are well described by…
An important problem in the theory of finite dynamical systems is to link the structure of a system with its dynamics. This paper contains such a link for a family of nonlinear systems over the field with two elements. For systems that can…
The threshold, or saturation phenomenon of spatially coupled systems is revisited in the light of Lyapunov's theory of dynamical systems. It is shown that an application of Lyapunov's direct method can be used to quantitatively describe the…