Related papers: Level statistics and localization transitions of L…
The question of the local stability of the (replica-symmetric) amorphous solid state is addressed for a class of systems undergoing a continuous liquid to amorphous-solid phase transition driven by the effect of random constraints. The…
We study the universal properties of eigenstate entanglement entropy across the transition between many-body localized (MBL) and thermal phases. We develop an improved real space renormalization group approach that enables numerical…
Quantum phase transitions are usually observed in ground states of correlated systems. Remarkably, eigenstate phase transitions can also occur at finite energy density in disordered, isolated quantum systems. Such transitions fall outside…
The dynamics of the eigenvalues (semimartingales) of a L\'{e}vy process $X$ with values in Hermitian matrices is described in terms of It\^{o} stochastic differential equations with jumps. This generalizes the well known Dyson-Brownian…
We investigate the statistics of eigenstates in a weak self-affine disordered potential in one dimension, whose Gaussian fluctuations grow with distance with a positive Hurst exponent $H$. Typical eigenstates are superlocalized on samples…
Based on the concept of self-decomposability, we extend some recent multivariate L\'evy models built using multivariate subordination with the aim of capturing situations in which a sudden event in one market is propagated onto related…
Contrary to the theoretical predictions that all waves in two-dimensional disordered materials are localized, Anderson localization is observed only for sufficiently high frequencies in an isotropically jammed two-dimensional disordered…
We provide an exact solution of large random arrowhead Hamiltonians with diagonal disorder, a minimal model for inhomogeneously broadened quantum emitters coupled to a cavity mode. We find that the distribution of energy spacing can be…
We consider a generalization of a one-dimensional stochastic process known in the physical literature as L\'evy-Lorentz gas. The process describes the motion of a particle on the real line in the presence of a random array of marked points,…
We consider a general class of high order weak approximation schemes for stochastic differential equations driven by L\'evy processes with infinite activity. These schemes combine a compound Poisson approximation for the jump part of the…
We develop a method that relates the truncated cumulant-function of the fourth order with the L\'evian cumulant-function. This gives us explicit formulas for the L\'evy-parameters, which allow a real-time analysis of the state of a…
It is well understood that, when numerically simulating SDEs with general noise, achieving a strong convergence rate better than $O(\sqrt{h})$ (where h is the step size) requires the use of certain iterated integrals of Brownian motion,…
Random walks are a fundamental model in applied mathematics and are a common example of a Markov chain. The limiting stationary distribution of the Markov chain represents the fraction of the time spent in each state during the stochastic…
This work is focused on the local eigenvalue statistics for the Anderson tight binding model with non-rank-one perturbations over the canopy tree, at large disorder. On the Hilbert space $\ell^2(\mathcal{C})$, where $ \mathcal{C} $ is the…
Models of many-body localization (MBL) exhibit slow numerical drifts towards delocalization with increasing system size, for which no satisfactory theory exists. Numerics indicates that these drifts are driven by the proliferation of…
In this paper, we present an overview of different types of random walk strategies with local and non-local transitions on undirected connected networks. We present a general approach to analyzing these strategies by defining the dynamics…
In this paper, we study the smallest non-zero eigenvalue of the sample covariance matrices $\mathcal{S}(Y)=YY^*$, where $Y=(y_{ij})$ is an $M\times N$ matrix with iid mean $0$ variance $N^{-1}$ entries. We prove a phase transition for its…
Process convolutions yield random fields with flexible marginal distributions and dependence beyond Gaussianity, but statistical inference is often hampered by a lack of closed-form marginal distributions, and simulation-based inference may…
Continuous time random walks combining diffusive and ballistic regimes are introduced to describe a class of L\'evy walks on lattices. By including exponentially-distributed waiting times separating the successive jump events of a walker,…
We consider highly heterogeneous random networks with symmetric interactions in the limit of high connectivity. A key feature of this system is that the spectral density of the corresponding ensemble exhibits a divergence within the bulk.…