Related papers: Exponential stochastic compression of one-dimensio…
The entanglement entropy in clean, as well as in random quantum spin chains has a logarithmic size-dependence at the critical point. Here, we study the entanglement of composite systems that consist of a clean and a random part, both being…
We study stochastic partial differential equations of the reaction-diffusion type. We show that, even if the forcing is very degenerate (i.e. has not full rank), one has exponential convergence towards the invariant measure. The convergence…
Probability estimation is essential for every statistical data compression algorithm. In practice probability estimation should be adaptive, recent observations should receive a higher weight than older observations. We present a…
We consider a class of stochastic growth models on the integer lattice which includes various interesting examples such as the number of open paths in oriented percolation and the binary contact path process. Under some mild assumptions, we…
This paper addresses the question of the fluctuations of the empirical entropy of a chain of infinite order. We assume that the chain takes values on a finite alphabet and loses memory exponentially fast. We consider two possible…
A one-dimensional diagonal tight binding electronic system with correlated disorder is investigated. The correlation of the random potential is exponentially decaying with distance and its correlation length diverges as the concentration of…
Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the…
We study kinetic and jamming properties of a space covering process in one dimension. The stochastic process is defined as follows: Seeds are nucleated randomly in space and produce rays which grow with a constant velocity. The growth stops…
In the context of infinitesimal strain plasticity with hardening, we derive a stochastic homogenization result. We assume that the coefficients of the equation are random functions: elasticity tensor, hardening parameter and flow-rule…
Disorder is a pervasive characteristic of natural systems, offering a wealth of non-repeating patterns. In this study, we present a novel storage method that harnesses naturally-occurring random structures to store an arbitrary pattern in a…
The model of binary aggregation with constant kernel is subjected to stochastic resetting: aggregates of any size explode into monomers at independent stochastic times. These resetting times are Poisson distributed, and the rate of the…
We measure stretched exponential behavior, exp(- (t/t_0)**beta), over many decades in a one-dimensional array of coupled chaotic electronic elements just above a crisis-induced intermittency transition. There is strong spatial heterogeneity…
Thermodynamic extensivity is commonly introduced as a postulate -- the homogeneity of degree one in thermodynamic potentials. We provide a constructive derivation of this property from microscopic conditions on the pair potential, without…
The interior of a living cell is an active, fluctuating, and crowded environment. Yet, it maintains a high level of coherent organization, which is readily apparent in the intracellular transport network. Membrane-bound compartments called…
We compute the density of states (d.o.s.) in N coupled chains with random hopping. At zero energy, the d.o.s. shows a singularity that strongly depends on the parity of N. For odd N, the d.o.s. is proportional to 1/(E (\ln |E|)^3), with and…
A disordered version of the one dimensional asymmetric exclusion model where the particle hopping rates are quenched random variables is studied. The steady state is solved exactly by use of a matrix product. It is shown how the phenomenon…
Recent generalizations of the Hopfield model of associative memories are able to store a number $P$ of random patterns that grows exponentially with the number $N$ of neurons, $P=\exp(\alpha N)$. Besides the huge storage capacity, another…
We investigate the distribution of the volume and coordination number associated to each particle in a jammed packing of monodisperse hard sphere using the mesoscopic ensemble developed in Nature 453, 606 (2008). Theory predicts an…
Taking into account the nonequivalence of fixed-force and fixed-length ensembles in the weak-force regime, equations of state are derived that describe the equilibrium extension or compression of an ideal Gaussian polymer chain in response…
We introduce a new model of preferential attachment with fitness, and establish a time reversed duality between the model and a system of branching-coalescing particles. Using this duality, we give a clear and concise explanation for the…