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Numerical study of the systematic error in Monte Carlo schemes for semiconductors

Orazio Muscato, Wolfgang Wagner, Vincenza Di Stefano (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The paper studies the convergence behavior of Monte Carlo schemes for semiconductors. A detailed analysis of the systematic error with respect to numerical parameters is performed. Different sources of systematic error are pointed out and illustrated in a spatially one-dimensional test case. The error with respect to the number of simulation particles occurs during the calculation of the internal electric field. The time step error, which is related to the splitting of transport and electric field...

Odd cutsets and the hard-core model on d

Ron Peled, Wojciech Samotij (2014)

Annales de l'I.H.P. Probabilités et statistiques

We consider the hard-core lattice gas model on d and investigate its phase structure in high dimensions. We prove that when the intensity parameter exceeds C d - 1 / 3 ( log d ) 2 , the model exhibits multiple hard-core measures, thus improving the previous bound of C d - 1 / 4 ( log d ) 3 / 4 given by Galvin and Kahn. At the heart of our approach lies the study of a certain class of edge cutsets in d , the so-called odd cutsets, that appear naturally as the boundary between different phases in the hard-core model. We provide a refined combinatorial...

On quenched and annealed critical curves of random pinning model with finite range correlations

Julien Poisat (2013)

Annales de l'I.H.P. Probabilités et statistiques

This paper focuses on directed polymers pinned at a disordered and correlated interface. We assume that the disorder sequence is a q -order moving average and show that the critical curve of the annealed model can be expressed in terms of the Perron–Frobenius eigenvalue of an explicit transfer matrix, which generalizes the annealed bound of the critical curve for i.i.d. disorder. We provide explicit values of the annealed critical curve for q = 1 and q = 2 and a weak disorder asymptotic in the general case....

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