Random walks constitute one of the cornerstone concepts in probability theory and statistical physics, representing a class of stochastic processes in which a moving entity takes successive steps in ...

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 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 ...

We consider a random walker on a d-regular graph. Starting from a fixed vertex, the first step is a unit step in any one of the d directions, with common probability 1/d for each one. At any later ...

Many theorists examine the behavior of stock prices, and the random walk hypothesis attempts to explain why stocks move the way they do. The random walk hypothesis states that stock market prices ...

Let {Xk: k ≥ 1} be a sequence of independent, identically distributed random variables with $EX_{1} = \mu < 0$. Form the random walk {Sn : n ≥ 0} by setting S0 ...

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 ...

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 ...