Lecture Notes and References

Sergio Ciliberto, Experimental aspects of large deviations

• Slides lecture 1
• Sides lecture 2

Bernard Derrida, Current fluctuations and transport in non-equilibrium systems

• Lecture 1
• Lecture 2
• Lecture 3
• Lecture 4
• Lecture 5
• Reference 1: Macroscopic fluctuation theory
• Reference 2: Non-equilibrium steady states: fluctuations and large deviations of the density and of the current

Evans, Stochastic resetting and large deviations

• Lecture notes

Alexander Hartmann, Numerical aspects of large deviations

• Slides
• Code1: mc_bernoulli.c
• Code2: bernoulli_direct.c
• Lecture notes

Pablo Hurtado, Large deviations and fluctuations paths

• References on Additivity Principle for current fluctuations:
  • Current fluctuations in non-equilibrium diffusive systems: an additivity principle
  • Weak additivity principle for current statistics in d-dimensions, Supp. Mat.
  • Structure of the optimal path to a fluctuation
• References on dynamical phase transitions in open systems:
  • Dynamical phase transitions in the current distribution of driven diffusive channels: Ref. 1, Ref. 2
  • Dynamical criticality in driven systems: non-perturbative results, microscopic origin and direct observation, Supp. Mat.
• References on dynamical phase transitions in closed systems:
  • Distribution of current in non-equilibrium diffusive systems and phase transitions
  • Spontaneous symmetry breaking at the fluctuating level
  • Dynamical phase transition for current statistics in a simple driven diffusive system
• References on time crystals and rare events:
  • Building continuous time crystals from rare events
  • Spectral signatures of symmetry-breaking dynamical phase transitions

Joachim Krug, Complexity and accessibility of random landscapes

• Slides
• Reference 1: Evolutionary accessibility of random and structured fitness landscapes
• Reference 2: Empirical fitness landscapes and the predictability of evolution

Vivien Lecomte, Large deviations in active systems

• Slides
• References

Baruch Meerson, Optimal fluctuation methods

• Slides lecture 1
• Slides lecture 2
• Reference 1: Airy distribution: Experiment, large deviations, and additional statistics
• Reference 2: Geometrical optics of constrained Brownian motion: three short stories
• Reference 3: WKB theory of large deviations in stochastic populations

Joachim Peinke, Rare events in turbulence and applications

• Slides

Valentina Ros, Complex Energy Landscapes

• Lecture notes

Herbert Spohn, Large deviation functionals from integrable many-body systems

• Slides

Hugo Touchette, A general introduction to large deviation theory from a physics point of view

you can find lecture notes here

Eric Vanden-Eijnden, Stochastic dynamics, rare events, and large deviations

• 1st Lecture
• 2nd Lecture
• 3rd Lecture
• 4th Lecture
• 5th Lecture
• Reference 1: Minimum-Action Method for Nonequilibrium Phase Transitions
• Reference 2: Numerical computation of rare events via large deviation theory
• Reference 3: Unveiling the Phase Diagram and Reaction Paths of the Active Model B with the Deep Minimum Action Method
• Reference 4: Large Deviations in Fast–Slow Systems
• Reference 5: Computing non-equilibrium trajectories by a deep learning approach
• Reference 6: Deep learning probability flows and entropy production rates in active matter
• Reference 7: Probability flow solution of the Fokker–Planck equation

Pierpaolo Vivo, Large deviations in random matrix theory and Coulomb gas systems

• Lecture notes
• Handout: a collection of reprinted papers/frontpages