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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

1 vote
Accepted

A tiling of $\mathbb{Z}^2$ from M. Barlow's paper

You have made a few copying errors ($T$ for $T^+$, for instance). For the tiling, my guess is that the claim is not that $\{ T(x) \, : \, x \in \mathbb{Z}^d \}$ is a tiling (that would be false), bu …
Sophie M's user avatar
  • 695
2 votes

Probabilistic problem on random spanning trees

This is not really an answer, but it's a suggestion of where to look for a counterexample. I played around for a few hours and couldn't quite get the parameters working, and it's possible they're unwo …
Sophie M's user avatar
  • 695
0 votes

Given an automatic set $S$ coming from a DFA $M$ when read little-endian, is $\overline{d}(S...

I believe the answer to Question 1 is positive, though maybe I've misunderstood something and the following sketch misses something important. For $n \in [1,N]$, the DFA halts and decides whether $n \ …
Sophie M's user avatar
  • 695
1 vote

Given an automatic set $S$ coming from a DFA $M$ when read little-endian, is $\overline{d}(S...

I'm posting a new answer because I think the discussion on my previous answer is helpful for understanding the edits to the question, and what I'm adding here is a complete rewrite and is much too lon …
Sophie M's user avatar
  • 695