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Tail estimates for norms of sums of log-concave random vectors
log-concave random vectors concentration inequalities deviation inequalities random matrices
2011/9/15
Abstract: We establish new tail estimates for order statistics and for the Euclidean norms of projections of an isotropic log-concave random vector. More generally, we prove tail estimates for the nor...
Sums of Ceiling Functions Solve Nested Recursions
Nested recursion Ceiling function Formal satisfaction Equivalence class
2011/9/15
Abstract: It is known that, for given integers s \geq 0 and j > 0, the nested recursion R(n) = R(n - s - R(n - j)) + R(n - 2j - s - R(n - 3j)) has a closed form solution for which a combinatorial inte...
Moments of random sums and Robbins' problem of optimal stopping
Moments of random sums Robbins' problem Probability
2011/9/13
Abstract: Robbins' problem of optimal stopping asks one to minimise the expected {\it rank} of observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the {\it value...
Compositions, Random Sums and Continued Random Fractions of Poisson and Fractional Poisson Processes
Fractional birth process Bell polynomials Mittag–Leffler functions Fibonacci numbers continued fractions Poisson random fields
2011/9/8
Abstract: In this paper we consider the relation between random sums and compositions of different processes. In particular, for independent Poisson processes $N_\alpha(t)$, $N_\beta(t)$, $t>0$, we sh...
Tangle sums and factorization of A-polynomials
Tangle sums factorization of A-polynomials Geometric Topology
2011/9/5
Abstract: We show that there exist infinitely many examples of pairs of knots, K_1 and K_2, that have no epimorphism $\pi_1(S^3\setminus K_1) \to \pi_1(S^3\setminus K_2)$ preserving peripheral structu...
The Knotting-Unknotting Game played on Sums of Rational Shadows
The Knotting-Unknotting Game Sums of Rational Shadows Combinatorics Geometric Topology
2011/9/5
Abstract: We consider the recently introduced knotting-unknotting game, in which two players take turns resolving crossings in a knot diagram which initially is missing all its crossing information. O...
An identity on the $2m$-th power mean value of the generalized Gauss sums
2m-th power mean exact calculating formula generalized quadratic Gauss sums Number Theory
2011/9/5
Abstract: In this paper, using combinatorial and analytic methods, we prove an exact calculating formula on the $2m$-th power mean value of the generalized quadratic Gauss sums for $m\geq 2$. This sol...
Malliavin Calculus and Self Normalized Sums
Malliavin calculus multiple stochastic integrals Steinn’s method self-normalized sums limit theorems
2011/8/23
Abstract: We study the self-normalized sums of independent random variables from the perspective of the Malliavin calculus. We give the chaotic expansion for them and we prove a Berry-Ess\'een bound w...
Sparse Sums of Positive Semidefinite Matrices
Sparse Sums Positive Semidefinite Matrices Combinatorics
2011/9/29
Abstract: Recently there has been much interest in "sparsifying" sums of rank one matrices: modifying the coefficients such that only a few are nonzero, while approximately preserving the matrix that ...
On the distribution of cubic exponential sums
Exponential sums Cubic theta functions Metaplectic forms
2011/8/23
Abstract: Using the theory of metaplectic forms,we study the asymptotic behavior of cubic exponential sums over the ring of Eisenstein integers. In the first part of the paper, some non-trivial estima...
Sums of alternating products of Riemann zeta values and solution of a Monthly problem
first Stieltjes constant Euler constant Riemann zeta function digamma function
2011/7/26
Abstract: We solve problem 11585 proposed by B. Burdick, AMM June-July 2011 {bf 118} (6), p. 558 for the sum of certain products of Riemann zeta function values. We further point out an alternating su...
On the sums of two cubes
sums two cubes
2011/2/28
We solve the equation f(x, y)3 + g(x, y)3 = x3 + y3 for homogeneous f, g ∈ C(x, y), completing an investigation begun by Vi`ete in 1591. The usual addition law for elliptic curves and composition give...
Congruences for central binomial sums and finite polylogarithms
Congruences central binomial sums finite polylogarithms
2011/1/19
(This is still a preliminary draft: the proofs are complete, but the exposition will be improved in the next version.) We prove congruences, modulo a power of a prime p, for certain finite sums involv...
On sums involving products of three binomial coefficients
Central binomial coefficients super congruences Catalan numbers
2011/1/21
In this paper we study congruences for sums of terms related to cubes of central binomial coefficients.
Some fascinating series and their sums
identities series sums algebraic and trigonometric series
2011/3/1
In this paper we present some interesting results involving summation of series in particular trigonometric ones.