22,037 research outputs found
Signature inversion for monotone paths
The aim of this article is to provide a simple sampling procedure to
reconstruct any monotone path from its signature. For every N, we sample a
lattice path of N steps with weights given by the coefficient of the
corresponding word in the signature. We show that these weights on lattice
paths satisfy the large deviations principle. In particular, this implies that
the probability of picking up a "wrong" path is exponentially small in N. The
argument relies on a probabilistic interpretation of the signature for monotone
paths
A measure of transcendence for singular points on conics
A singular point on a plane conic defined over is a
transcendental point of the curve which admits very good rational
approximations, uniformly in terms of the height. Extremal numbers and Sturmian
continued fractions are abscissa of such points on the parabola . In
this paper we provide a measure of transcendence for singular points on conics
defined over which, in these two cases, improves on the measure
obtained by Adamczewski et Bugeaud. The main tool is a quantitative version of
Schmidt subspace theorem due to Evertse.Comment: 8 page
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