Statistical Physics and Computation in High Dimension
Talkat Probability, Geometry, and Computation in High Dimensions Boot Camp (Simons Institute, Fall 2020) · 2020-08-19..08-28·
summary
Computes typical minimal energy per spin for the random‑field Ising model in the n→∞ limit and shows the average free energy equals the extremum of a replica potential, using the replica method heuristically and then proving it with Guerra interpolation plus a constrained‑partition trick; finds the saddle‑point equation m = E[tanh(β(h+m))] and the β→∞ limit for ground‑state energy. Also derives an iterative solver whose state evolution matches that fixed point via approximate message passing, and proves the replica prediction is exact for this model.
AI-written summary · about
chapters (12)
- 0:00Introduction
- 4:10Sampling
- 7:05Minimize
- 8:45Random Financial Model
- 14:48Replicameter
- 16:00How does it work
- 18:08Computation
- 21:58Replica symmetric assumption
- 26:28Ex extremum
- 42:48Algorithm
- 47:31Exercise
- 55:57QA
related talks
01h 06mTutorial: Methods from Statistical Physics II
01h 17mPedagogical Talk: Random Optimisation Problems
39mPhase Retrieval in High Dimensions: Statistical and Computational Phase Transitions
26mTight Algorithmic Thresholds for Spin Glass Hamiltonians
24mA subpolynomial-time algorithm for the free energy of one-dimensional...
01h 07mConsensus-Based Interacting Particle Systems and Mean-field PDEs for Optimization and Sampling
45mTAP Free Energy, Spin Glasses, and Variational Inference
59mTutorial: Methods from Statistical Physics I