000			01784nam a22002177a 4500
005			20251211114602.0
020			_a978-1-009-30511-2
037			_aBC_731 27 _fbroch
040			_aBC-ENSA _bfre
041			_aang _bang
080			_a519.2
100			_aROCH Sébastien
245			_aModern discrete probability _ban essential toolkit
260			_aUited Kingdom _bCambridge University Press _c2024
300			_a452 p. _bcouv. en coul. _c26 cm
520			_aProviding a graduate-level introduction to discrete probability and its applications, this book develops a toolkit of essential techniques for analysing stochastic processes on graphs, other random discrete structures, and algorithms. Topics covered include the first and second moment methods, concentration inequalities, coupling and stochastic domination, martingales and potential theory, spectral methods, and branching processes. Each chapter expands on a fundamental technique, outlining common uses and showing them in action on simple examples and more substantial classical results. The focus is predominantly on non-asymptotic methods and results. All chapters provide a detailed background review section, plus exercises and signposts to the wider literature. Readers are assumed to have undergraduate-level linear algebra and basic real analysis, while prior exposure to graduate-level probability is recommended. This much-needed broad overview of discrete probability could serve as a textbook or as a reference for researchers in mathematics, statistics, data science, computer science and engineering.
541			_cACHN
562			_e1 exemplaire(s)
650			_aPROBABILITE/ANALYSE/ALGORITHME/ALGEBRE LINEAIRE/THEORIE DES GRAPHES
942			_c09
999			_c36433 _d64431