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, ...

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 ...

We study the asymptotic behavior of a multidimensional random walk in a general cone. We find the tail asymptotics for the exit time and prove integral and local limit theorems for a random walk ...

For many financial professionals, Burton Malkiel's classic has served as a trusted guide for nearly 50 years. Many investors use it to understand how markets work. This review takes a closer look at ...

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 ...