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Exact solution of a 1d asymmetric exclusion model using a matrix formulation
Several recent works have shown that the one-dimensional fully asymmetric exclusion model, which describes a system of particles hopping in a preferred direction with hard core interactions, can be
Random networks of automata: a simple annealed approximation
This work gives a simple annealed approximation which predicts K = 2 as the critical value of K and gives also quantitative predictions for distances between iterated configurations.
Random-Energy Model: Limit of a Family of Disordered Models
In this Letter, a simple model of disordered systems---the random-energy model---is introduced and solved. This model is the limit of a family of disordered models, when the correlations between the
Shift in the velocity of a front due to a cutoff
We consider the effect of a small cutoff $\ensuremath{\varepsilon}$ on the velocity of a traveling wave in one dimension. Simulations done over more than ten orders of magnitude as well as a simple
Non-equilibrium steady states: fluctuations and large deviations of the density and of the current
These lecture notes give a short review of methods such as the matrix ansatz, the additivity principle or the macroscopic fluctuation theory, developed recently in the theory of non-equilibrium
Optimal storage properties of neural network models
The authors calculate the number, p= alpha N of random N-bit patterns that an optimal neural network can store allowing a given fraction f of bit errors and with the condition that each right bit is
Polymers on disordered trees, spin glasses, and traveling waves
We show that the problem of a directed polymer on a tree with disorder can be reduced to the study of nonlinear equations of reaction-diffusion type. These equations admit traveling wave solutions
An exact solution of a one-dimensional asymmetric exclusion model with open boundaries
A simple asymmetric exclusion model with open boundaries is solved exactly in one dimension. The exact solution is obtained by deriving a recursion relation for the steady state: if the steady state