An essential companion for advanced undergraduate and graduate level courses in probability, this book describes the tools and results that are used extensively in the field and has worked examples, ...

Will a certain tritium atom decay by a certain time? According to our current science, this question concerning physical phenomena should be answered by sampling from a probability distribution, a ...

Branching processes in random environments (BPREs) extend classical Galton–Watson models by allowing the reproduction law to vary according to a sequence of random factors. In each generation, the ...

When the mathematicians Jeff Kahn and Gil Kalai first posed their “expectation threshold” conjecture in 2006, they didn’t believe it themselves. Their claim — a broad assertion about mathematical ...

Probability underpins AI, cryptography and statistics. However, as the philosopher Bertrand Russell said, “Probability is the most important concept in modern science, especially as nobody has the ...

Random processes take place all around us. It rains one day but not the next; stocks and bonds gain and lose value; traffic jams coalesce and disappear. Because they’re governed by numerous factors ...