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) ...

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 ...

The dynamics of many natural and artificial systems are well described as random walks on a network: the stochastic behaviour of molecules, traffic patterns on the internet, fluctuations in stock ...

We test the random-walk hypothesis for the Indian stock market by applying three unit root tests with two structural breaks. We find that unit root tests that allow for two structural breaks alone are ...

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.

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 ...

Mathematicians from the California Institute of Technology have solved an old problem related to a mathematical process called a random walk. The team, which also worked with a colleague from Israel’s ...