uniform distribution theory

The uniform distributions puzzle by

1. Uniform distribution mod one At primary school the first author was taught to estimate the area of a (convex) body by drawing it on a piece of graph paper, and then counting the number of (unit) squares inside. There is obviously a little ambiguity in deciding how to count the squares which

ii The von Mises distribution is often useful for modelling circular data problems. We con-sider a model for which von Mises data is contaminated with a certain proportion of points uniformly distributed around the circle. Maximum likelihood estimation is used to produce parameter estimates

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The uniform distribution is an important counterexample in game theory as many of the canonical game dynamics have been shown not to converge to the equilibrium in certain cases. In particular none of the canonical game dynamics converge to the uniform distribution in a form of rock

Abstract. In this paper, we propose the definition of a measure for sets of strings of length not greater than a given number. This measure leads to an instanciation of the uniform distribution definition in sets of such limited-size strings, for which we provide a linear time complexity generative

In this paper we continue the investigation into the group of algebras with uniformly distributed invariants U(K), and its relation to the Schur subgroup, undertaken in [9]. The notation is the same as in [9]. In the first section we investigate the index 1 U(K), : S(K), 1 where q is an

In this paper it is shown that the sequence {py} (p runs through the prime numbers) is uniformly distributed mod 1, if y is greater than one and not an integer. The method used here is a modification of that of Pjateckij-Shapiro in [1], to estimate the sum 2\<P«2N e{kpy). 1.

Let E be a (modular!) elliptic curve over Q, of conductor N. Let K denote an imaginary quadratic field of discriminant D, with (N, D) = 1. If p is a prime, then there exists a unique Zp-extension K∞/K such that Gal(K/Q) acts nontrivially on Gal(K∞/K). The field K ∞ is called the anticyclotomic Zp-extension of K. Let E(K∞) denote the Mordell-Weil group of E over K∞. Then a fundamental