Balance Functions, Correlations, Charge Fluctuations and Interferometry

Connections between charge balance functions, charge fluctuations and correlations are presented. It is shown that charge fluctuations can be directly expressed in terms of a balance functions under certain assumptions. The distortion of charge balance functions due to experimental acceptance is discussed and the effects of identical boson interference is illustrated with a simple model.Comment: 1 eps figure included. 5 pages in revtex

A quantitative central limit theorem for linear statistics of random matrix eigenvalues

It is known that the fluctuations of suitable linear statistics of Haar distributed elements of the compact classical groups satisfy a central limit theorem. We show that if the corresponding test functions are sufficiently smooth, a rate of convergence of order almost $1/n$ can be obtained using a quantitative multivariate CLT for traces of powers that was recently proven using Stein's method of exchangeable pairs.Comment: Title modified; main result stated under slightly weaker conditions; accepted for publication in the Journal of Theoretical Probabilit

The Characteristic Polynomial of a Random Permutation Matrix at Different Points

We consider the logarithm of the characteristic polynomial of random permutation matrices, evaluated on a finite set of different points. The permutations are chosen with respect to the Ewens distribution on the symmetric group. We show that the behavior at different points is independent in the limit and are asymptotically normal. Our methods enables us to study more general matrices, closely related to permutation matrices, and multiplicative class functions.Comment: 30 pages, 2 figures. Differences to Version 1: We have improved the presentation and add some references Stochastic Processes and their Applications, 201

Ewens measures on compact groups and hypergeometric kernels

On unitary compact groups the decomposition of a generic element into product of reflections induces a decomposition of the characteristic polynomial into a product of factors. When the group is equipped with the Haar probability measure, these factors become independent random variables with explicit distributions. Beyond the known results on the orthogonal and unitary groups (O(n) and U(n)), we treat the symplectic case. In U(n), this induces a family of probability changes analogous to the biassing in the Ewens sampling formula known for the symmetric group. Then we study the spectral properties of these measures, connected to the pure Fisher-Hartvig symbol on the unit circle. The associated orthogonal polynomials give rise, as $n$ tends to infinity to a limit kernel at the singularity.Comment: New version of the previous paper "Hua-Pickrell measures on general compact groups". The article has been completely re-written (the presentation has changed and some proofs have been simplified). New references added

Functional limit theorems for random regular graphs

Consider d uniformly random permutation matrices on n labels. Consider the sum of these matrices along with their transposes. The total can be interpreted as the adjacency matrix of a random regular graph of degree 2d on n vertices. We consider limit theorems for various combinatorial and analytical properties of this graph (or the matrix) as n grows to infinity, either when d is kept fixed or grows slowly with n. In a suitable weak convergence framework, we prove that the (finite but growing in length) sequences of the number of short cycles and of cyclically non-backtracking walks converge to distributional limits. We estimate the total variation distance from the limit using Stein's method. As an application of these results we derive limits of linear functionals of the eigenvalues of the adjacency matrix. A key step in this latter derivation is an extension of the Kahn-Szemer\'edi argument for estimating the second largest eigenvalue for all values of d and n.Comment: Added Remark 27. 39 pages. To appear in Probability Theory and Related Field

Evaluation of a chemoresponse assay as a predictive marker in the treatment of recurrent ovarian cancer: Further analysis of a prospective study

BACKGROUND: Recently, a prospective study reported improved clinical outcomes for recurrent ovarian cancer patients treated with chemotherapies indicated to be sensitive by a chemoresponse assay, compared with those patients treated with non-sensitive therapies, thereby demonstrating the assay's prognostic properties. Due to cross-drug response over different treatments and possible association of in vitro chemosensitivity of a tumour with its inherent biology, further analysis is required to ascertain whether the assay performs as a predictive marker as well. METHODS: Women with persistent or recurrent epithelial ovarian cancer (n=262) were empirically treated with one of 15 therapies, blinded to assay results. Each patient's tumour was assayed for responsiveness to the 15 therapies. The assay's ability to predict progression-free survival (PFS) was assessed by comparing the association when the assayed therapy matches the administered therapy (match) with the association when the assayed therapy is randomly selected, not necessarily matching the administered therapy (mismatch). RESULTS: Patients treated with assay-sensitive therapies had improved PFS vs patients treated with non-sensitive therapies, with the assay result for match significantly associated with PFS (hazard ratio (HR)=0.67, 95% confidence interval (CI)=0.50–0.91, P=0.009). On the basis of 3000 simulations, the mean HR for mismatch was 0.81 (95% range=0.66–0.99), with 3.4% of HRs less than 0.67, indicating that HR for match is lower than for mismatch. While 47% of tumours were non-sensitive to all assayed therapies and 9% were sensitive to all, 44% displayed heterogeneity in assay results. Improved outcome was associated with the administration of an assay-sensitive therapy, regardless of homogeneous or heterogeneous assay responses across all of the assayed therapies. CONCLUSIONS: These analyses provide supportive evidence that this chemoresponse assay is a predictive marker, demonstrating its ability to discern specific therapies that are likely to be more effective among multiple alternatives

Phase transitions in quantum chromodynamics

The current understanding of finite temperature phase transitions in QCD is reviewed. A critical discussion of refined phase transition criteria in numerical lattice simulations and of analytical tools going beyond the mean-field level in effective continuum models for QCD is presented. Theoretical predictions about the order of the transitions are compared with possible experimental manifestations in heavy-ion collisions. Various places in phenomenological descriptions are pointed out, where more reliable data for QCD's equation of state would help in selecting the most realistic scenario among those proposed. Unanswered questions are raised about the relevance of calculations which assume thermodynamic equilibrium. Promising new approaches to implement nonequilibrium aspects in the thermodynamics of heavy-ion collisions are described.Comment: 156 pages, RevTex. Tables II,VIII,IX and Fig.s 1-38 are not included as postscript files. I would like to ask the requestors to copy the missing tables and figures from the corresponding journal-referenc

Second order efficiency of the MLE with respect to any bounded bowl-shape loss function

Let X1, X2, .. be a sequence of i.i.d. random variables, each having density f(x, θ0) where {f(x, θ)} is a family of densities with respect to a dominating measure µ. Suppose n½(θˆ - θ) and n½(T - θ), where θˆ is the mle and T is any other efficient estimate, have Edgeworth expansions up to o(n-1) uniformly in a compact neighbourhood of θ0. Then (under certain regularity conditions) one can choose a function c(θ) such that θˆ = θˆ + c(θˆ)/n satisfies Pθ0 {-x1< n½(θˆ' - θ0)(I(θ0))½ < x2} > Pθ0 {-x1< n½(T - θ0)(I(θ0))½ < x2} + o(n-1), for all x1, x2 > 0. This result implies the second order efficiency of the mle with respect to any bounded loss function Ln(θ, a) = h(n½(a - θ)), which is bowl-shaped i.e., whose minimum value is zero at a - θ = 0 and which increases as |a - θ| increases. This answers a question raised by C. R. Rao (Discussion on Professor Efron's paper)