Related papers: Multifractality and statistical localization in th…
Level statistics of systems that undergo many--body localization transition are studied. An analysis of the gap ratio statistics from the perspective of inter- and intra-sample randomness allows us to pin point differences between…
Although much of the focus of statistical works on networks has been on static networks, multiple networks are currently becoming more common among network data sets. Usually, a number of network data sets, which share some form of…
The Boltzmann-Gibbs probability distributions generated by logarithmically correlated random potentials provide a simple yet nontrivial example of disorder-induced multifractal measures. We introduce and discuss two analytically tractable…
The escape probability $\xi_{x}$ from a site $x$ of a one-dimensional disordered lattice with trapping is treated as a discrete dynamical evolution by random iterations over nonlinear maps parametrized by the right and left jump…
We make the first steps towards generalizing the theory of stochastic block models, in the sparse regime, towards a model where the discrete community structure is replaced by an underlying geometry. We consider a geometric random graph…
We study thermally activated, low temperature equilibrium dynamics of elastic systems pinned by disorder using one loop functional renormalization group (FRG). Through a series of increasingly complete approximations, we investigate how the…
Since the seminal work of Anderson, localisation has been recognised as a standard mechanism allowing quantum many-body systems to escape ergodicity. This idea acquired even more prominence in the last decade as it has been argued that…
Over the past three decades, describing the reality surrounding us using the language of complex networks has become very useful and therefore popular. One of the most important features, especially of real networks, is their complexity,…
In the framework of a one-dimensional model with a tightly localized self-attractive nonlinearity, we study the formation and transfer (dragging) of a trapped mode by "nonlinear tweezers", as well as the scattering of coherent linear wave…
We investigate the spectral and transport properties of a two-arm tight-binding ladder perturbed by an external magnetic field following an Aubry-Andr\'e-Harper profile. The varying magnetic flux trapped in consecutive ladder-cells…
We consider the general character of the spatial distribution of a population that grows through reproduction and subsequent local resettlement of new population members. We present several simple one and two-dimensional point placement…
Quantifying how spatial disorder affects the movement of a diffusing particle or agent is fundamental to target search studies. When diffusion occurs on a network, that is on a highly disordered environment, we lack the mathematical tools…
We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be…
Statistical analysis of the eigenfunctions of the Anderson tight-binding model with on-site disorder on regular random graphs strongly suggests that the extended states are multifractal at any finite disorder. The spectrum of fractal…
This paper revisits the classical concept of network modularity and its spectral relaxations used throughout graph data analysis. We formulate and study several modularity statistic variants for which we establish asymptotic distributional…
The nearest-neighbor Aubry-Andr\'e quasiperiodic localization model is generalized to include power-law translation-invariant hoppings $T_l\propto t/l^a$ or power-law Fourier coefficients $W_m \propto w/m^b$ in the quasi-periodic potential.…
The interaction between transitivity and sparsity, two common features in empirical networks, implies that there are local regions of large sparse networks that are dense. We call this the blessing of transitivity and it has consequences…
Current questions in ecology revolve around instabilities in the dynamics on spatial networks and particularly the effect of node heterogeneity. We extend the Master Stability Function formalism to inhomogeneous biregular networks having…
Motivated by the role that spectral properties play for the dynamical evolution of a quantum many-body system, we investigate the level spacing statistic of the extended Bose-Hubbard model. In particular, we focus on the distribution of the…
A phenomenon of racial segregation in U.S. cities is a multifaceted area of study. A recent advancement in this field is the development of a methodology that transforms census population count-by-race data into a grid of monoracial cells.…