Complete Convergence of the Maximum Partial Sums for Arrays of Rowwise of AANA Random Variables

The limiting behavior of the maximum partial sums | is investigated, and some new results are obtained, where { , ≥ 1, ≥ 1} is an array of rowwise AANA random variables and { , ≥ 1} is a sequence of positive real numbers. As an application, the Chung-type strong law of large numbers for arrays of rowwise AANA random variables is obtained. The results extend and improve the corresponding ones of Hu and Taylor (1997) for arrays of rowwise independent random variables

Complete Convergence for Moving Average Process of Martingale Differences

Under some simple conditions, by using some techniques such as truncated method for random variables (see e.g., Gut (2005)) and properties of martingale differences, we studied the moving process based on martingale differences and obtained complete convergence and complete moment convergence for this moving process. Our results extend some related ones

Strong Convergence Properties for Asymptotically Almost Negatively Associated Sequence

By applying the moment inequality for asymptotically almost negatively associated (in short AANA) random sequence and truncated method, we get the three series theorems for AANA random variables. Moreover, a strong convergence property for the partial sums of AANA random sequence is obtained. In addition, we also study strong convergence property for weighted sums of AANA random sequence

On a new concept of stochastic domination and the laws of large numbers

Consider a sequence of positive integers $\{k_n,n\ge1\}$, and an array of nonnegative real numbers $\{a_{n,i},1\le i\le k_n,n\ge1\}$ satisfying $\sup_{n\ge 1}\sum_{i=1}^{k_n}a_{n,i}=C_0\in (0,\infty).$ This paper introduces the concept of $\{a_{n,i}\}$-stochastic domination. We develop some techniques concerning this concept and apply them to remove an assumption in a strong law of large numbers of Chandra and Ghosal [Acta. Math. Hungarica, 1996]. As a by-product, a considerable extension of a recent result of Boukhari [J. Theoret. Probab., 2021] is established and proved by a different method. The results on laws of large numbers are new even when the summands are independent. Relationships between the concept of $\{a_{n,i}\}$-stochastic domination and the concept of $\{a_{n,i}\}$-uniform integrability are presented. Two open problems are also discussed.Comment: 26 page

On Complete Convergence for Weighted Sums of ρ

We prove the strong law of large numbers for weighted sums ∑i=1n‍aniXi, which generalizes and improves the corresponding one for independent and identically distributed random variables and φ-mixing random variables. In addition, we present some results on complete convergence for weighted sums of ρ*-mixing random variables under some suitable conditions, which generalize the corresponding ones for independent random variables

Complete Moment Convergence for Arrays of Rowwise -Mixing Random Variables

We investigate the complete moment convergence for maximal partial sum of arrays of rowwise -mixing random variables under some more general conditions. The results obtained in the paper generalize and improve some known ones

HIV prevention while bulldozers roll: developing evidence based HIV prevention intervention for female sex workers following the demolition of Goa’s redlight area

Background: Interventions targeting female sex workers (FSWs) are pivotal to HIV prevention in India. Societal factors and legislation around sex-work are potential barriers to achieving this. In recent years several high profile closures of red-light areas and dance bars in India have occurred. In this thesis I describe the effects of the demolition of Goa’s red-light area on the organsiation of sex-work, HIV risk environment, and implications for evidence-based HIV prevention. Methods: The pre-demolition phase was a detailed ethnographic study. The early post-demolition phase included rapid ethnographic mapping of sex-work in the immediate aftermath. The late post-demolition phase was a cross-sectional survey supplemented by an in-depth qualitative study. 326 FSWs were recruited throughout Goa using respondent-driven-sampling, and completed interviewer-administered questionnaires. They were tested for sexually transmitted infections (STIs) and HIV. Results: The homogeneous brothel-based sex-work in Goa evolved into heterogeneous, clandestine and dispersed types of sex-work. The working environment was higher risk and less conducive to HIV prevention. Infections were common with 25.7% prevalence of HIV and 22.5% prevalence of curable STIs. Women who had never worked in Baina, young women, and those who had recently started sex-work were particularly likely to have curable STIs, a marker of recent sexual risk. STIs were independently associated with young age, lack of schooling, no financial autonomy, deliberate-self-harm, sexual-abuse, regular customers, streetbased sex-work, Goan ethnicity, and being asymptomatic. Having knowledge about HIV, access to free STI services, and having an intimate partner were associated with a lower likelihood of STIs. HIV was independently associated with being Hindu, recent migration to Goa, lodge or brothel-based sex work, and dysuria. Conclusions: Tackling structural and gender-based determinants of HIV are integral to HIV prevention strategies. Prohibition and any form of criminalisation of sex-work reduce the sex workers’ agency and create barriers to effective HIV prevention

3D Quantum Gravity from Holomorphic Blocks

Three-dimensional gravity is a topological field theory, which can be quantized as the Ponzano-Regge state-sum model built from the $\{3nj\}$-symbols of the recoupling of the \SU(2) representations, in which spins are interpreted as quantized edge lengths in Planck units. It describes the flat spacetime as gluing of three-dimensional cells with a fixed boundary metric encoding length scale. In this paper, we revisit the Ponzano-Regge model formulated in terms of spinors and rewrite the quantum geometry of 3D cells with holomorphic recoupling symbols. These symbols, known as Schwinger's generating function for the $\{6j\}$-symbols, are simply the squared inverse of the partition function of the 2D Ising model living on the boundary of the 3D cells. They can furthermore be interpreted, in their critical regime, as scale-invariant basic elements of geometry. We show how to glue them together into a discrete topological quantum field theory. This reformulation of the path integral for 3D quantum gravity, with a rich pole structure of the elementary building blocks, opens a new door toward the study of phase transitions and continuum limits in 3D quantum gravity, and offers a new twist on the construction of a duality between 3D quantum gravity and a 2d conformal theory.Comment: 42 pages + appendices, 18 figure