We consider a ballistic random walk in an i.i.d. random environment that does not allow retreating in a certain fixed direction. Homogenization and regeneration techniques combine to prove a law of large numbers and an averaged invariance principle. The assumptions are non-nestling and 1 + ε (resp. 2 + ε) moments for the step of the walk uniformly in the environment, for the law of large number...

We discuss the potential of neutrinoless double beta decay for testing Lorentz invariance and the weak equivalence principle as well as contributions from dilaton exchange gravity in the neutrino sector. While neutrino oscillation bounds constrain the region of large mixing of the weak and gravitational eigenstates, we obtain new constraints on violations of Lorentz invariance and the equivalen...

We consider a discrete time random walk in a space-time i.i.d. random environment. We use a martingale approach to show that the walk is diffusive in almost every fixed environment. We improve on existing results by proving an invariance principle and considering environments with an L2 averaged drift. We also state an a.s. invariance principle for random walks in general random environments wh...

We analyze the emergence of a minimal length for a large class of generalized commutation relations, preserving commutation of the position operators and translation invariance as well as rotation invariance (in dimension higher than one). We show that the construction of the maximally localized states based on squeezed states generally fails. Rather, one must resort to a constrained variationa...

This paper addresses invariance principles for a certain class of switched nonlinear systems. We provide an extension of LaSalle’s Invariance Principle for these systems and state asymptotic stability criteria. We also present some related results that deal with the compactness of the trajectories of these switched systems and that are interesting by their own.

This is part of a research program to establish a unified field model for interactions in nature. The aim of this article is to postulate a new principle of representation invariance (PRI), to provide a needed mathematical foundation for PRI, and to use PRI to refine the unified field equations of four interactions. Intuitively, PRI amounts to saying that all SU(N) gauge theories should be inva...

Invariance principles underlie many key theories in modern science. They provide the explanatory and predictive framework necessary for the rigorous study of natural phenomena ranging from the structure of crystals, to magnetism, to relativistic mechanics. Vigo (2008, 2009) introduced a new general notion and principle of invariance from which two parameter-free (ratio and exponential) models w...

Let (Xi)i∈Z be a regular stationary process for a given filtration. The weak invariance principle holds under the condition ∑ i∈Z ‖P0(Xi)‖2 < ∞ (see [11], [2], [3]). In this paper, we show that this criterion is independent of other known criteria: the martingalecoboundary decomposition of Gordin (see [7], [8]), the criterion of Dedecker and Rio (see [4]) and the condition of Maxwell and Woodro...

We study some stochastic models of physical mapping of genomic sequences. Our starting point is a global construction of the process of the clones and of the process of the anchors which are used to map the sequence. This yields explicit formulas for the moments of the proportion occupied by the anchored clones, even in inhomogeneous models. This also allows to compare, in this respect, inhomog...