Numerical analysis for linear constant-coefficient multi-step Finite Difference schemes is a
longstanding topic, developed approximately fifty years ago. It relies on the stability of the …

We prove the linear orbital stability of spectrally stable stationary discrete shock profiles for
conservative finite difference schemes applied to systems of conservation laws. The proof …

In this article, we study the pointwise asymptotic behavior of iterated convolutions on the one
dimensional lattice Z. We generalize the so-called local limit theorem in probability theory to …

We establish in this paper the logarithmic Bramson correction for Fisher-KPP equations on
the lattice $\mathbb {Z} $. The level sets of solutions with step-like initial conditions are …

Numerical analysis for linear constant-coefficients Finite Difference schemes was developed
approximately fifty years ago. It relies on the assumption of scheme stability and in particular …

We give a complete expansion, at any accuracy order, for the iterated convolution of a
complex valued integrable sequence in one space dimension. The remainders are …

Sensory perception (eg, vision) relies on a hierarchy of cortical areas, in which neural
activity propagates in both directions, to convey information not only about sensory inputs …

In this paper, we prove that, under precise spectral assumptions, some finite difference
approximations of scalar leftgoing transport equations on the positive half-line with …

The local (central) limit theorem precisely describes the behavior of iterated convolution
powers of a probability distribution on the d-dimensional integer lattice, Z d. Under certain …

We consider certain constant-coefficient differential operators on R d that have positive-
definite symbols. Each such operator Λ with symbol P defines a semigroup of operators e− t …