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Exact solution of a 1d asymmetric exclusion model using a matrix formulation
- B. Derrida, M. Evans, V. Hakim, V. Pasquier
- Mathematics
- 7 April 1993
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-energy model: An exactly solvable model of disordered systems
- B. Derrida
- Physics
- 1 September 1981
Random networks of automata: a simple annealed approximation
- B. Derrida, Y. Pomeau
- Computer Science
- 15 January 1986
TLDR
Random-Energy Model: Limit of a Family of Disordered Models
- B. Derrida
- Mathematics
- 14 July 1980
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
- É. Brunet, B. Derrida
- Mathematics
- 1 September 1997
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
- B. Derrida
- Physics
- 28 March 2007
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…
AN EXACTLY SOLUBLE NON-EQUILIBRIUM SYSTEM : THE ASYMMETRIC SIMPLE EXCLUSION PROCESS
- B. Derrida
- Physics
- 1 July 1998
Optimal storage properties of neural network models
- E. Gardner, B. Derrida
- Computer Science
- 7 January 1988
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
- B. Derrida, H. Spohn
- Materials Science
- 1 June 1988
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
- B. Derrida, E. Domany, D. Mukamel
- Physics, Mathematics
- 1 November 1992
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…
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