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1 results

  • 7 - Random Walkers

  • Luca Leuzzi, National Research Council of Italy, Enzo Marinari, Sapienza Università di Roma, Giorgio Parisi, Sapienza Università di Roma
  • Book:
    Probability Theory for Quantitative Scientists
    Published online:
    24 July 2025
    Print publication:
    14 August 2025, pp 188-216

  • Summary

    In this chapter we study the first example of a correlated memoryless phenomenon: the famous “drunkard’s walk”, formally termed the random walk. We begin from a very simple case, in a homogeneous and isotropic space on a discrete hypercubic lattice. Then we add traps here and there. Eventually we make a foray into the continuous regime, with the Fokker–Planck diffusion equation (which, we see, is what physicists call a Schrödinger equation in imaginary time), and the stochastic differential Langevin equation.