Related papers: Extreme value distributions and Renormalization Gr…
While averages and typical fluctuations often play a major role to understand the behavior of a non-equilibrium system, this nonetheless is not always true. Rare events and large fluctuations are also pivotal when a thorough analysis of the…
The present paper studies the limiting behavior of the average score of a sequentially selected group of items or individuals, the underlying distribution of which, $F$, belongs to the Gumbel domain of attraction of extreme value…
We provide asymptotic theory for the joint distribution of $X_{\mathrm{inv}}$ and $X_{\mathrm{des}}$, the numbers of inversions and descents of random permutations. Recently, D\"orr & Kahle (2022) proved that $X_{\mathrm{inv}}$,…
We show how the interplay of non-linear dynamics, self-gravity, and fluctuations leads to self-affine behavior of matter density correlations quite generically, i.e., with a power-law exponent whose value does not depend in a very direct…
The proposed paper discusses the problem of discrimination between close hypotheses about distributions belonging to the Gumbel maximum domain of attraction. The distinctive feature of the proposed work is using only k higher order…
We employ the machinery of smooth scaling and coarse-graining of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) to make a rigorous renormalisation group…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
The transverse-field Ising models with random exchange interactions in finite dimensions are investigated by means of a real-space renormalization-group method. The scheme yields the exact values of the critical point and critical exponent…
Advanced science and technology provide a wealth of big data from different sources for extreme value analysis. Classical extreme value theory was extended to obtain an accelerated max-stable distribution family for modelling competing…
Estimation of extreme conditional quantiles is often required for risk assessment of natural hazards in climate and geo-environmental sciences and for quantitative risk management in statistical finance, econometrics, and actuarial…
Extreme value theory provides rigorous theory and statistical tools for extrapolation in machine learning, particularly in settings where traditional methods struggle due to data scarcity in the tails. A broad range of tasks benefit from…
In this paper, we consider the problem of estimating an extreme quantile of a Weibull tail-distribution. The new extreme quantile estimator has a reduced bias compared to the more classical ones proposed in the literature. It is based on an…
In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems that have a singular measure. Using the block maxima approach described in Faranda et al. [2011] we show that,…
We explore fundamental questions about the renormalization group through a detailed re-examination of Feigenbaum's period doubling route to chaos. In the space of one-humped maps, the renormalization group characterizes the behavior near…
Approximation only by derivative (or more generally momentum) expansions, combined with reparametrization invariance, turns the continuous renormalization group for quantum field theory into a set of partial differential equations which at…
This paper addresses the problem of estimating the extreme value index in presence of random censoring for distributions in the Weibull domain of attraction. The methodologies introduced in [Worms (2014)], in the heavy-tailed case, are…
Let $X_1$, $X_2$,... be a sequence of independent random variables with common distribution function $F$ in the domain of attraction of a Gumbel extreme value distribution and for each integer $n\geq 1$, let $X_{1,n} \leq ... X_{n,n}$…
We use point processes theory to describe the asymptotic distribution of all upper order statistics for observations collected at renewal times. As a corollary, we obtain limiting theorems for corresponding extremal processes.
Irreversible aggregation is revisited in view of recent work on renormalization of complex networks. Its scaling laws and phase transitions are related to percolation transitions seen in the latter. We illustrate our points by giving the…
We consider three classes of linear differential equations on distribution functions, with a fractional order $\alpha\in [0,1].$ The integer case $\alpha =1$ corresponds to the three classical extreme families. In general, we show that…