Related papers: Anderson localization and extreme values in chaoti…
We prove localization (near the bottom of the spectrum) for certain non-stationary variants of the Anderson model in three dimensions. More specifically, we prove a Wegner estimate, which implies localization by existing work. Two key…
We introduce the concept of geometric extremal graphical models, which are defined through the gauge function of the limit set obtained from suitably scaled random vectors in light-tailed margins. For block graphs, we prove results relating…
For Anderson localization on the Cayley tree, we study the statistics of various observables as a function of the disorder strength $W$ and the number $N$ of generations. We first consider the Landauer transmission $T_N$. In the localized…
Understanding the complex structure of multivariate extremes is a major challenge in various fields from portfolio monitoring and environmental risk management to insurance. In the framework of multivariate Extreme Value Theory, a common…
We study non-stationary stochastic processes arising from sequential dynamical systems built on maps with a neutral fixed points and prove the existence of Extreme Value Laws for such processes. We use an approach developed in \cite{FFV16},…
Motivated by the link between Anderson localisation on high-dimensional graphs and many-body localisation, we study the effect of periodic driving on Anderson localisation on random trees. The time dependence is eliminated in favour of an…
We study Anderson localisation on high-dimensional graphs with spatial structure induced by long-ranged but distance-dependent hopping. To this end, we introduce a class of models that interpolate between the short-range Anderson model on a…
The coarse spatial resolution of gridded climate models, such as general circulation models, limits their direct use in projecting socially relevant variables like extreme precipitation. Most downscaling methods estimate the conditional…
We use the recently developed finite cluster typical medium approach to study the Anderson localization transition in three dimensions. Applying our method to the box and binary alloy disorder distributions, we find a fast convergence with…
Many environmental processes such as rainfall, wind or snowfall are inherently spatial and the modelling of extremes has to take into account that feature. In addition, environmental processes are often attached with an angle, e.g., wind…
Extreme value analysis (EVA) uses data to estimate long-term extreme environmental conditions for variables such as significant wave height and period, for the design of marine structures. Together with models for the short-term evolution…
We have investigated the valence transition in the extended periodic Anderson model (EPAM) within the framework of dynamical mean field theory. Previous theoretical studies have indicated the presence of this transition in parameter ranges…
We investigate light transport in three-dimensional disordered media composed of irregular dielectric particles using large scale full-wave simulations. For subwavelength particles with size parameter $kr \approx 1$ and high refractive…
In a disordered environment, the probability of transmission of a wave reduces with increasing disorder, the ultimate limit of which is the near-zero transmission due to Anderson localization. Under localizing conditions, transport is…
Machine learning is vital in high-stakes domains, yet conventional validation methods rely on averaging metrics like mean squared error (MSE) or mean absolute error (MAE), which fail to quantify extreme errors. Worst-case prediction…
Deep learning-based trajectory prediction models for autonomous driving often struggle with generalization to out-of-distribution (OOD) scenarios, sometimes performing worse than simple rule-based models. To address this limitation, we…
Extreme value analysis is an essential methodology in the study of rare and extreme events, which hold significant interest in various fields, particularly in the context of environmental sciences. Models that employ the exceedances of…
A one-dimensional boundary of a two-dimensional topological superconductor can host a number of topologically protected chiral modes. Combining two topological superconductors with different topological indices, it is possible to achieve a…
We observe a singularity in the electronic properties of the Anderson Model of Localization with bounded diagonal disorder, which is clearly distinct from the well-established mobility edge (localization-delocalization transition) that…
Wave propagation in disordered media can be strongly modified by multiple scattering and wave interference. Ultimately the so-called Anderson-localized regime is reached when the waves become strongly confined in space. So far, Anderson…