An Introduction to Probability Theory and its Applications, Volume I

TL;DR: In this paper, a strategy for modelisation macroscopique probabiliste du couplage entre fissuration and transferts de fluides dans les structures en beton arme is presented.

TL;DR: In this article, the authors considered non-negative integer-valued autoregressive processes where the autoregression parameter is close to unity and obtained the local asymptotic structure of the likelihood ratios of the model, showing that the limit experiment is Poissonian.

TL;DR: In this article, the authors studied the machine interference problem consisting of M operating machines and an unreliable server who leaves for a vacation of random length when there are no failed machines queuing up for repair in the repair facility.

TL;DR: In this paper, the authors give fairly elementary proofs for the threshold theorem due to Williams (1971) and Whittle (1955) based on an application of the reflection principle through the ballot problem.

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.