Displaying similar documents to “Limit laws for transient random walks in random environment on ℤ ”

On the Newcomb-Benford law in models of statistical data.

Tomás Hobza, Igor Vajda (2001)

Revista Matemática Complutense

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We consider positive real valued random data X with the decadic representation X = Σ D 10 and the first significant digit D = D(X) in {1,2,...,9} of X defined by the condition D = D ≥ 1, D = D = ... = 0. The data X are said to satisfy the Newcomb-Benford law if P{D=d} = log(d+1 / d) for all d in {1,2,...,9}. This law holds for example for the data with logX uniformly distributed on an interval (m,n) where m and n are integers. We show that if logX has a distribution...

Sign changes of error terms related to arithmetical functions

Paulo J. Almeida (2007)

Journal de Théorie des Nombres de Bordeaux

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Let H ( x ) = ∑ n ≤ x φ ( n ) n - 6 π 2 x . Motivated by a conjecture of Erdös, Lau developed a new method and proved that # { n ≤ T : H ( n ) H ( n + 1 ) < 0 } ≫ T . We consider arithmetical functions f ( n ) = ∑ d ∣ n b d d whose summation can be expressed as ∑ n ≤ x f ( n ) = α x + P ( log ( x ) ) + E ( x ) , where P ( x ) is a polynomial, E ( x ) = - ∑ n ≤ y ( x ) b n n ψ x n + o ( 1 ) and ψ ( x ) = x - ⌊ x ⌋ - 1 / 2 . We generalize Lau’s method and prove results about the number of sign changes for these error terms.