Juggling competing demands in a network of feverishly calculating computers drawing on the same memory resources is like trying to avert collisions among blindfolded, randomly zigzagging ice skaters.

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) ...

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 walk hypothesis suggests stock market movements are unpredictable, impacting active trading. This theory supports long-term investment strategies, like buy-and-hold, over short-term speculation ...

Consider a sequence ($X_{k}\colon k\geq 0$) of regularly varying independent and identically distributed random variables with mean 0 and finite variance. We develop ...