The random walk theorem, first presented by French mathematician Louis Bachelier in 1900 and then expanded upon by economist Burton Malkiel in his 1973 book A Random Walk Down Wall Street, asserts ...

Random walks and percolation theory form a fundamental confluence in modern statistical physics and probability theory. Random walks describe the seemingly erratic movement of particles or entities, ...

The Annals of Probability, Vol. 2, No. 2 (Apr., 1974), pp. 347-348 (2 pages) Let $\{X_n, n \geqq 1\}$ be a stationary independent sequence of real random variables ...

Random walks in random environments constitute a pivotal area of research at the interface of probability theory, statistical physics and mathematical modelling. This field investigates stochastic ...

Theory that stock price changes from day to day are accidental or haphazard; changes are independent of each other and have the same probability distribution. For a simple random walk, the best ...

Voters' preferences depend on available information. Following Case-Based Decision Theory, we assume that this information is processed additively. We prove that the collective preferences deduced ...