Related papers: Achlioptas processes are not always self-averaging

The dynamics of an order parameter's amplitude and phase determines the collective behaviour of novel states emerged in complex materials. Time- and momentum-resolved pump-probe spectroscopy, by virtue of its ability to measure material…

This note proves an upper bound for the fluctuations of a second-class particle in the totally asymmetric simple exclusion process. The proof needs a lower tail estimate for the last-passage growth model associated with the exclusion…

Tracking tracer particles in heterogeneous environments plays an important role in unraveling the material properties. These heterogeneous structures are often static and depend on the sample realizations. Sample-to-sample fluctuations of…

We study Bernoulli bond percolation on a random recursive tree of size $n$ with percolation parameter $p(n)$ converging to $1$ as $n$ tends to infinity. The sizes of the percolation clusters are naturally stored in a tree. We prove…

The use of degree-degree correlations to model realistic networks which are characterized by their Pearson's coefficient, has become widespread. However the effect on how different correlation algorithms produce different results on…

We present a stochastic evolutionary model obtained through a perturbation of Kauffman's maximally rugged model, which is recovered as a special case. Our main results are: (i) existence of a percolation-like phase transition in the finite…

Percolation is a paradigmatic model in disordered systems and has been applied to various natural phenomena. The percolation transition is known as one of the most robust continuous transitions. However, recent extensive studies have…

Percolation is a concept widely used in many fields of research and refers to the propagation of substances through porous media (e.g., coffee filtering), or the behaviour of complex networks (e.g., spreading of diseases). Percolation…

The universal behaviour of the directed percolation universality class is well understood, both the critical scaling as well as finite size scaling. This article focuses on the block (finite size) scaling of the order parameter and its…

We numerically simulate the uniform athermal shearing of bidisperse, frictionless, two dimensional spherocylinders and three dimensional prolate ellipsoids. We focus on the orientational ordering of particles as an asphericity parameter…

We consider paradigmatic quenched disordered quantum spin models, viz., the XY spin glass and random-field XY models, and show that quenched averaged quantum correlations can exhibit the order-from-disorder phenomenon for finite-size…

We introduce a new oriented evolving graph model inspired by biological networks. A node is added at each time step and is connected to the rest of the graph by random oriented edges emerging from older nodes. This leads to a statistical…

Lack of self-averaging originates in many disordered models from a fragmentation of the phase space where the sizes of the fragments remain sample-dependent in the thermodynamic limit. On the basis of new results in percolation theory, we…

We discuss the universal scaling laws of order parameter fluctuations in any system in which the second-order critical behaviour can be identified. These scaling laws can be derived rigorously for equilibrium systems when combined with the…

Percolation theory and the associated conductance networks have provided deep insights into the flow and transport properties of a vast number of heterogeneous materials and media. In practically all cases, however, the conductance of the…

Co-evolutionary adaptive mechanisms are not only ubiquitous in nature, but also beneficial for the functioning of a variety of systems. We here consider an adaptive network of oscillators with a stochastic, fitness-based, rule of…

We consider percolation on high-dimensional product graphs, where the base graphs are regular and of bounded order. In the subcritical regime, we show that typically the largest component is of order logarithmic in the number of vertices.…

We consider bond percolation on random graphs with given degrees and bounded average degree. In particular, we consider the order of the largest component after the random deletion of the edges of such a random graph. We give a rough…

We study the percolation properties of force networks in an anisotropic model for granular packings, the so-called q-model. Following the original recipe of Ostojic et al. [Nature 439, 828 (2006)], we consider a percolation process in which…

Percolation processes on random networks have been the subject of intense research activity over the last decades: the overall phenomenology of standard percolation on uncorrelated and unclustered topologies is well known. Still some…