Some Questions of Interest

Here are some (of many) math problems/topics I am currently interested in. Some of these, I think about more actively, while others only from time to time. I try to gradually elaborate on each of these problems. If you have any answer, idea or comment, I would be very glad to hear.

  • Metastability in the hard-core models [+/-]

  • Phase transitions and stability against noise in cellular automata and tilings [+/-]

  • The “central limit theorem” of finite (or compact) groups [+/-]

  • Do deterministic cellular automata obey the 2nd law of thermodynamics? [+/-]

  • Invariant measures of cellular automata with sufficiently chaotic behavior [+/-]

  • Some questions about strongly transitive cellular automata (Update: August 2, 2013)

  • Do “typical” configurations exist? [+/-]

  • First-order transitions and breaking of translation symmetry in lattice models [+/-]
      (December 29, 2013)

  • Statistical mechanics description of quasicrystals [+/-]

  • Coupling method for random fields and Markov processes on them [+/-]

  • Matching, couplings, transportation, joinings, ... [+/-]

  • Do the conservation laws of reversible cellular automata have a decidable theory? [+/-]

  • Does every particle-conserving cellular automaton have a particle flow? [+/-]

  • Banach-Tarski paradox for coin tosses [+/-]

  • ...

Last Update: January 2015