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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.
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$\mathbb{P}(d(X,Y)>\alpha)<\beta$ 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
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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. …
- 395
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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 …
- 395
3
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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
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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 …
5
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1
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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 …
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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 …
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