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Results tagged with pr.probability
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user 78164
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
11
votes
3
answers
590
views
Proofs of main probability results from other fields
Making connections between different areas is very exciting and probability has already made connections with other fields (BM used in proving complex analysis and PDE results).
To keep it short, I wi …
- 4,529
4
votes
0
answers
190
views
Remaining models conjectured to converge to SLE(6) or CLE(6)
I am wondering which models are conjectured (eg. numerically) to converge to SLE(6) (Schramm-Loewner evolution with $\kappa=6$) or CLE(6) (conformal loop ensemble). I am searching for a research topic …
- 3,597
3
votes
0
answers
87
views
Random Voronoi percolation to SLE($\kappa$), for which $\kappa$?
Random Voronoi percolation is described in "The critical probability for random Voronoi percolation in the plane is 1/2" .
They mention that Schramm and Benjamini, showed a form of conformal invarian …
- 395
2
votes
1
answer
182
views
Percolation on the hyperbolic plane and convergence to SLE(6) on hyperbolic plane
In "Percolation in the hyperbolic plane" the authors study the properties of percolation in the hyperbolic plane. Smirnov and others proved convergence of isotropic percolation to SLE(6).
Do these r …
- 8,992
1
vote
2
answers
343
views
Coding SLEs (Schramm–Loewner Evolution) eg. SLE(6)
Any references/links on codes for SLEs written in C++ or Matlab that I can run in Windows (visual studio)?
The only code I found was:http://math.arizona.edu/~tgk/research.html but the link was empty. …
- 1,791
5
votes
1
answer
442
views
Importance of Ornstein's isomorphism theorem
"Perhaps the most important parts of the Ornstein theory are criteria for determining whether or not a shift or flow is Bernoulli (a Bernoulli shift, $B_{ct}$ , or $B_{t}^{\infty}$) because it allows …
- 1,590
1
vote
0
answers
121
views
$\mathbb{P}(d(X,Y)>\alpha)<\beta$ if $\mathbb{P}(X\in E)\leq \mathbb{P}(Y\in E^{\alpha})+\be...
Given two random variables X,Y with measures P,Q. Show that if $P(E) \le Q(E^\alpha) + \beta$ for all measurable $E\subset\mathbb{R}$ then $\mathbb{P}(d(X,Y)>\alpha)<\beta$.
Only hints please.
Atte …
- 395