An Introduction to Probability Theory and its Applications, Volume I

TL;DR: A novel message authentication code based on the recently proposed NTMAC structure, called CRC-NTMAC, for noisy message authentication, which replaces the truncated conventional MACs by cyclic redundancy check (CRC) codes in its constructions as the sub-MACs.

TL;DR: The Polya posterior has been developed as a noninformative Bayesian approach to survey sampling as discussed by the authors, and it is appropriate when little or no prior information about the population is available.

TL;DR: In this article, the authors analyze group decision-making in situations in which members discuss the value of a continuous random variable, then take an up-ordown vote based on their assessments of the continuous variable.

TL;DR: By determining subleading corrections in a large interval asymptotics, the applicability of conformal field theory predictions at criticality is tested, and a universal interpolation formula is derived based on the solution of a Painlevé V equation for the full counting statistics of the transverse magnetization and the domain walls.

TL;DR: This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.

TL;DR: This work addresses the problem of predicting a word from previous words in a sample of text and discusses n-gram models based on classes of words, finding that these models are able to extract classes that have the flavor of either syntactically based groupings or semanticallybased groupings, depending on the nature of the underlying statistics.

TL;DR: In this article, the authors present a case study of non-normal distribution and non-commutative joint distributions and define a set of basic combinatorics, such as non-crossing partitions, sum-of-free random variables, and products of free random variables.

TL;DR: This chapter explains why many real-world networks are small worlds and have large fluctuations in their degrees, and why Probability theory offers a highly effective way to deal with the complexity of networks, and leads us to consider random graphs.