Related papers: Localization transition, Lifschitz tails and rare-…
We resolve an existing question concerning the location of the mobility edge for operators with a hopping term and a random potential on the Bethe lattice. The model has been among the earliest studied for Anderson localization, and it…
We consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. This model is known to exhibit a phase transition: If $d \ge 3$ and the environment is "not too random", then, the total…
This thesis presents original results in two domains of disordered statistical physics: logarithmic correlated Random Energy Models (logREMs), and localization transitions in long-range random matrices. In the first part devoted to logREMs,…
The study of network data in the social and health sciences frequently concentrates on two distinct tasks (1) detecting community structures among nodes and (2) associating covariate information to edge formation. In much of this data, it…
We propose a simple model of the evolution of a social network which involves local search and volatility (random decay of links). The model captures the crucial role the network plays for information diffusion. This is responsible for a…
We compare localization properties of one-dimensional Frenkel excitons with Gaussian and Lorentzian uncorrelated diagonal disorder. We focus on the states of the Lifshits tail, which dominate the optical response and low-temperature energy…
We study the phase transition from the persistence phase to the extinction phase for the SIRS (susceptible/ infected/ refractory/ susceptible) model of diseases spreading on random networks. By studying temporal evolution and…
The ideas of mathematical topology play an important role in many aspects of modern physics - from phase transitions to field theory to nonlinear dynamics (Nakahara M (2003) in Geometry, Topology and Physics, ed Brewer DF (IOP Publishing…
It is argued that topological disorder in amorphous solids can be described by local strains related to local reference crystals and local rotations. An intuitive localization criterion is formulated from this point of view. The Inverse…
Minimally twisted bilayer graphene in the presence of an interlayer bias develops a triangular network of valley chiral modes that propagate along the $AB/BA$ interfaces and scatter at the $AA$ regions. The low energy physics of the…
We study a family of binary state, socially-inspired contagion models which incorporate imitation limited by an aversion to complete conformity. We uncover rich behavior in our models whether operating with either probabilistic or…
We study the hierarchical analogue of power-law random band matrices, a symmetric ensemble of random matrices with independent entries whose variances decay exponentially in the metric induced by the tree topology on $\mathbb{N}$. We map…
Preferential attachment is a central paradigm in the theory of complex networks. In this contribution we consider various generalizations of preferential attachment including for example node removal and edge rewiring. We demonstrate that…
A two-level system subjected to a high-frequency driving field can exhibit an effect termed ``coherent destruction of tunneling'', in which the tunneling of the system is suppressed at certain values of the frequency and strength of the…
In epidemiological modelling, dynamics on networks, and in particular adaptive and heterogeneous networks have recently received much interest. Here we present a detailed analysis of a previously proposed model that combines heterogeneity…
We study preferential attachment mechanisms in random graphs that are parameterized by (i) a constant bias affecting the degree-biased distribution on the vertex set and (ii) the distribution of times at which new vertices are created by…
To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…
In the study of randomly connected neural network dynamics there is a phase transition from a `simple' state with few equilibria to a `complex' state characterised by the number of equilibria growing exponentially with the neuron…
The superconducting properties of a two-dimensional superconducting wire network with a new geometry have been measured as a function of the external magnetic field. The extreme localization effect recently predicted for this periodic…
A weakly disordered quasi-one-dimensional tight-binding hopping model with $N$ rows is considered. The probability distribution of the Landauer conductance is calculated exactly in the middle of the band, $\epsilon=0$, and it is shown that…