The Net Advance of Physics:
RANDOM WALKS AND CURVES

RANDOM WALK PROBLEM and RANDOM CURVES:

• General: Introductory:
  • Chemotaxis: How a Small Organism Finds a Food Source by Andrea Schmidt [On Mehran Kardar's stat mech homepage at MIT] Random walk for high-school students.

• General:
  • An Introduction to Non-diffusive Transport Models by Alexandre Bovet [2015/08]
  • Random walks: A review of algorithms and applications by F. Xia et al. [2020/08]

• Type: CONTINUOUS-TIME:
  • The Continuous Time Random Walk: Still Trendy by Ryszard Kutner and Jaume Masoliver [2016/12] "Fifty-year history, state of art, and outlook."

• Type: LÉVY FLIGHTS:
  • Radiation trapping and Lévy flights in atomic vapours: an introductory review by Martine Chevrollier [Contemporary Physics 53, 227 (2013)]
  • Lévy walks by V. Zaburdaev et al. [2014/10]
  • Lévy Processes For Finance: An Introduction In R by Derek J. Manuge [2015/03]
  • An Introduction to Non-diffusive Transport Models by Alexandre Bovet [2015/08]
  • Search for Food of Birds, Fish and Insects by Rainer Klages [2018/04]

• Type:NON-GAUSSIAN:
  • Radiation trapping and Lévy flights in atomic vapours: an introductory review by Martine Chevrollier [Contemporary Physics 53, 227 (2013)]

• Type: ONE-DIMENSIONAL: Kimball and Frisch 2006/06;

• Type: QUANTUM: Kempe 2003/03;
  • Quantum Walks by Daniel Reitzner et al. [Acta Physica Slovaca 61, 603 (2011)]
  • Quantum walks: a comprehensive review by Salvador E. Venegas-Andraca [2012/01]

• Type: QUANTUM: Re: COMPUTATION:
  • How to compute using quantum walks by V. Kendon [2020/04]
  • Review on quantum-walk computing: Theory, implementation, and application by X.-G. Qiang et al. [2024/04]

• Type: QUANTUM: Re: DECOHERENCE: Kendon 2006/06;

• Type: QUANTUM: Re: TOPOLOGY:
  • Topological phenomena in quantum walks; elementary introduction to the physics of topological phases by Takuya Kitagawa [2011/12]

• Type: IN RANDOM ENVIRONMENTS: Zeitouni 2003/04;

• Type: SELF AVOIDING:
  • Self-avoiding walks and polygons -- an overview by Anthony J. Guttmann [2012/12]

• Type: TWO-DIMENSIONAL: Werner 2003/03;

• Aspects: RATCHETS:
  • Brownian motion and gambling: from ratchets to paradoxical games by J. M. R. Parrondo and Luis Dinis [Contemporary Physics 45, 147 (2004)]

• Aspects: SCHRAMM-LOEWNER EVOLUTIONS: Werner 2003/03;

• Re: BIOLOGY:
  • The Boltzmann factor, DNA melting, and Brownian ratchets: Topics in an introductory physics sequence for biology and premedical students by S. G. J. Mochrie [2011/05]
  • 100 years after Smoluchowski: stochastic processes in cell biology by David Holcman and Zeev Schuss [2016/12]

• Re: ELECTRICAL NETWORKS: Doyle and Snell 1984;
  • Recent progress on the Random Conductance Model by Marek Biskup [2011/12]

• Re: FRACTIONAL CALCULUS:
  • The Random Walk's Guide to Anomalous Diffusion: A Fractional Dynamics Approach by Ralf Metzler and Joseph Klafter [Physics Reports 339, 1 (2000)] PDF

• Re: KNOT THEORY: Nechaev 98/12;
• Re: SCHRAMM-LOEWNER THEORY: Gruzberg and Kadanoff 2003/09;

THE NET ADVANCE OF PHYSICS