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Decay of correlations in stochastic quantization: the exponential Euclidean field in two dimensions
We present two approaches to establish the exponential decay of correlation functions of Euclidean quantum field theories (EQFTs) via stochastic...
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Quenched Decay of Correlations for One-dimensional Random Lorenz Maps
We study rates of mixing for small random perturbations of one-dimensional Lorenz maps. Using a random tower construction, we prove that, for Hölder...
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On the Strong Forms of the Borel–Cantelli Lemma and Dynamical Systems with Polynomial Decay of Correlations
AbstractThe strong forms of the Borel–Cantelli lemma are variants of the strong law of large numbers for sums of event indicators while the series of...
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Strong biological correlations as a cause of autonomous oscillations in epidemics
We consider the impact of strong biological correlations on the epidemic process. The biological correlations mean the influence of the environment...
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Almost Sure Invariance Principle for Random Distance Expanding Maps with a Nonuniform Decay of Correlations
We prove a quenched almost sure invariance principle for certain classes of random distance expanding dynamical systems which do not necessarily...
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Inhomogeneous long-range percolation in the weak decay regime
We study a general class of percolation models in Euclidean space including long-range percolation, scale-free percolation, the weight-dependent...
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Correlations, Shapes, and Fragmentations of Ultracold Matter
This 2022 report summarizes our activities at the HLRS facilities (Hawk) in the framework of the multiconfigurational time-dependent Hartree for...
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Exponential decay of transverse correlations for O(N) spin systems and related models
We prove exponential decay of transverse correlations in the Spin O ( N ) model for arbitrary non-zero values of the external magnetic field and...
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Optimal decay of the parabolic semigroup in stochastic homogenization for correlated coefficient fields
We study the large scale behavior of elliptic systems with stationary random coefficient that have only slowly decaying correlations. To this aim we...
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The Unification of Evolutionary Dynamics through the Bayesian Decay Factor in a Game on a Graph
We unify evolutionary dynamics on graphs in strategic uncertainty through a decaying Bayesian update. Our analysis focuses on the Price theorem of...
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Subcritical Gaussian multiplicative chaos in the Wiener space: construction, moments and volume decay
We construct and study properties of an infinite dimensional analog of Kahane’s theory of Gaussian multiplicative chaos (Kahane in Ann Sci Math...
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Extensions of the Classical Percolation Model
The classical percolation model described in Chap. 2 is appropriate when there are no correlations between...
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Invariant measures for the strong-facilitated exclusion process
Consider a generalized model of the facilitated exclusion process, which is a one-dimensional exclusion process with a dynamical constraint that...
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Exponential Decay in the Loop O(n) Model on the Hexagonal Lattice for n > 1 and \(x<\tfrac {1}{\sqrt {3}}+\varepsilon (n)\)
We show that the loop O(n) model on the hexagonal lattice exhibits exponential decay of loop sizes whenever n > 1 and...
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Credit Modelling*
In this chapter, we study the case of default in credit modelling. Structural models and intensity models are first covered. We then study the...
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Stationary Reversible Processes of a Moving Average and Autorepression with Residuals as a Moving Average
AbstractIn this paper, we show how to select an adequate model of a stationary reversible moving-average process of finite order, given the...
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Quantitative weak mixing for interval exchange transformations
We establish a dichotomy for the rate of the decay of the Cesàro averages of correlations of sufficiently regular functions for typical interval...
