Event-scale analysis techniques using correlation and fluctuation measuresare applied to heavy-ion collision data with the goal of discovering,characterizing, and understanding deconfined quark matter. In service of thesegoals development of a scale-local thermodynamics is discussed and applied to abroad range of toy models, simulations, and data. Scale-local partitioning isdiscussed at length and an ideal theoretical reference is derived forcomparison to data. The dimension of the chaotic attractor of the Henon map iscalculated as a function of scale, and the implications of scale-localdimension are explored. Event spaces with discriminatory power are developedand applied to the face recognition problem, detector triggering, and STAR andNA49 data. Event-wise mean transverse momentum fluctuations in STAR data areanalyzed with a minimally biased central-limit based measure using numericaland graphical methods. Cut efficiencies, corrections, and systematic errorsources are all addressed. A connection between non-statistical fluctuationsand two-particle correlations is found and exploited. Two-particle correlationspace formation is discussed and methods for minimizing error from event mixingare discovered. Central data from STAR and NA49 are analyzed, confirming theresults of the fluctuation analysis and providing additional insight into thephysics sources contributing to correlations in heavy-ion collisions.
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