Hitting probabilities for non-convex lattice

Probabilities of hitting a convex hull

In this note, we consider the non-negative least square method with a random matrix. This problem has connections with the probability that the origin is not in the convex hull of many random points. As related problems, suitable estimates are obtained as well on the probability that a small ball does not hit the convex hull. Abstract Dans cette Note nous appliquons la méthode des moindres carr...

Hitting probabilities and large deviations

Let ”Yn•n∈Z+ be a sequence of random variables in R d and let A ⊂ Rd: Then P”Yn ∈ A for some n• is the hitting probability of the set A by the sequence ”Yn•. We consider the asymptotic behavior, as m → ∞, of P”Yn ∈ mA; some n• = P”hitting mA• whenever (1) the probability law of Yn/n satisfies the large deviation principle and (2) the central tendency of Yn/n is directed away from the given set ...

On fuzzy convex lattice-ordered subgroups

In this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. Also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. Furthermore,...

2078 Hitting Probabilities and Large Deviations

Jarník’s convex lattice n-gon for non-symmetric norms

What is the minimum perimeter of a convex lattice n-gon? This question was answered by Jarník in 1926. We solve the same question, and prove a limit shape result, in the case when perimeter is measured by a (not necessarily symmetric) norm.