Random walks constitute a fundamental model in probability theory, widely employed to elucidate diffusion processes and random fluctuations in disordered systems. The Gaussian free field (GFF) ...

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 ...

An interesting paper making the point that you can too forecast foreign exchange rates. Not, of course, at the hour to hour level where people speculate at leverage of 500:1, but over longer time ...

Why is it that when you walk randomly, the more you walk, the farther you get from your starting point?

For a random walk with drift, the best forecast of tomorrow's price is today's price plus a drift term. One could think of the drift as measuring a trend in the price (perhaps reflecting long-term ...