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We study analytically and numerically the extreme value distribution of observables defined along the temporal evolution of a dynamical system. The convergence to the Gumbel law of observable recurrences gives information on the fractal…

Dynamical Systems · Mathematics 2020-12-02 Théophile Caby , Davide Faranda , Sandro Vaienti , Pascal Yiou

We consider the range of a one-parameter family of self-interacting walks on the integers up to the time of exit from an interval. We derive the weak convergence of an appropriately scaled range. We show that the distribution functions of…

Probability · Mathematics 2014-07-28 Kazuki Okamura

In this paper, we analyse a sub-class of two-dimensional homogeneous nearest neighbour (simple) random walk restricted on the lattice using the matrix geometric approach. In particular, we first present an alternative approach for the…

Probability · Mathematics 2017-07-21 Stella Kapodistria , Zbigniew Palmowski

We study the distribution of vortex lines in a three-dimensional lattice with inhomogeneous couplings. We investigate the spatial distribution of the number of vortex lines, showing how the vortex lines are expelled from the region with…

Statistical Mechanics · Physics 2011-11-16 Mauro Iazzi , Nicola Bassan , Andrea Trombettoni , Kevin E. Schmidt , Stefano Fantoni

Two-term asymptotic formulae for the probability distribution functions for the smallest eigenvalue of the Jacobi $ \beta $-Ensembles are derived for matrices of large size in the r\'egime where $ \beta > 0 $ is arbitrary and one of the…

Probability · Mathematics 2024-01-24 B. Winn

The extreme value statistics of active matter offer significant insight into their unique properties. A phase transition has recently been reported in a model of branching run-and-tumble particles, describing the spatial spreading of an…

Statistical Mechanics · Physics 2020-06-11 Bertrand Lacroix-A-Chez-Toine , Asaf Miron

Properties of networks are often characterized in terms of features such as node degree distributions, average path lengths, diameters, or clustering coefficients. Here, we study shortest path length distributions. On the one hand, average…

Social and Information Networks · Computer Science 2015-01-20 Christian Bauckhage , Kristian Kersting , Fabian Hadiji

The low temperature physics of disordered systems is governed by the statistics of extremely low energy states. It is thus rather important to discuss the possible universality classes for extreme value statistics. We compare the usual…

Disordered Systems and Neural Networks · Physics 2009-10-30 J. P. Bouchaud , M. Mezard

We give an infinitesimal criterion, in the analytic setting, for a vector space to be locally homogeneous under some group action. Our approach differs from those which resort to an inverse function theorem (e.g. those of Moser, Zehnder or…

Dynamical Systems · Mathematics 2011-10-12 Jacques Féjoz , Mauricio Garay

In this paper we define distributions on moment spaces corresponding to measures on the real line with an unbounded support. We identify these distributions as limiting distributions of random moment vectors defined on compact moment spaces…

Probability · Mathematics 2012-11-14 Holger Dette , Jan Nagel

We study the shortest vector lengths in module lattices over arbitrary number fields, with an emphasis on cyclotomic fields. In particular, we sharpen the techniques of arXiv:2308.15275v2 to establish improved results for the variance of…

Number Theory · Mathematics 2025-10-16 Nihar Gargava , Vlad Serban , Maryna Viazovska , Ilaria Viglino

Extreme value theory is part and parcel of any study of order statistics in one dimension. Our aim here is to consider such large sample theory for the maximum distance to the origin, and the related maximum "interpoint distance," in…

Probability · Mathematics 2015-10-30 Sreenivasa Rao Jammalamadaka , Svante Janson

We study a new family of random variables, that each arise as the distribution of the maximum or minimum of a random number $N$ of i.i.d.~random variables $X_1,X_2,\ldots,X_N$, each distributed as a variable $X$ with support on $[0,1]$. The…

Statistics Theory · Mathematics 2014-03-07 Jie Hao , Anant Godbole

We develop and generalize the theory of extreme value for non-stationary stochastic processes, mostly by weakening the uniform mixing condition that was previously used in this setting. We apply our results to non-autonomous dynamical…

Dynamical Systems · Mathematics 2017-06-27 Ana Cristina Moreira Freitas , Jorge Milhazes Freitas , Sandro Vaienti

We study the distribution of maxima (Extreme Value Statistics) for sequences of observables computed along orbits generated by random transformations. The underlying, deterministic, dynamical system can be regular or chaotic. In the former…

Dynamical Systems · Mathematics 2015-06-11 Davide Faranda , Jorge Milhazes Freitas , Valerio Lucarini , Giorgio Turchetti , Sandro Vaienti

The present paper establishes upper and lower bounds on the speed of approximation in a wide range of natural Diophantine approximation problems. The upper and lower bounds coincide in many cases, giving rise to optimal results in…

Number Theory · Mathematics 2014-07-11 Anish Ghosh , Alex Gorodnik , Amos Nevo

Several statistical problems, such as multiple heterogeneous graph analysis, distributed PCA, integrative data analysis, and simultaneous dimension reduction of images, can involve a collection of $m$ matrices whose leading subspaces…

Statistics Theory · Mathematics 2025-12-10 Runbing Zheng , Minh Tang

We study the transmission of random walkers through a finite-size inhomogeneous material with a quenched, long-range correlated distribution of scatterers. We focus on a finite one-dimensional structure where walkers undergo random…

Statistical Mechanics · Physics 2014-07-22 Piercesare Bernabó , Raffaella Burioni , Stefano Lepri , Alessandro Vezzani

We study the motion of independent particles in a dynamical random environment on the integer lattice. The environment has a product distribution. For the multidimensional case, we characterize the class of spatially ergodic invariant…

Probability · Mathematics 2018-09-20 Mathew Joseph , Firas Rassoul-Agha , Timo Seppäläinen

We discuss spreading estimates for dynamical systems given by the iteration of an extended CMV matrix. Using a connection due to Cantero--Gr\"unbaum--Moral--Vel\'azquez, this enables us to study spreading rates for quantum walks in one…

Mathematical Physics · Physics 2016-03-04 David Damanik , Jake Fillman , Darren C. Ong