Sentence examples for free probability from inspiring English sources
Carter (2010) gives an example from free probability theory.
What are the compact forms of these functions for q = 0 (free probability case)?
Our technique is based on stochastic calculus, large deviations, and elements from free probability.
We also prove an analogous result in the setting of free probability.
They are of current interest, in part because of their connections with free probability and engineering systems theory.
Recently, connections between type B and infinitesimal free probability were put into evidence by Belinschi and Shlyakhtenko [S.T. Belinschi, D. Shlyakhtenko, Free probability of type B: Analytic aspects and applications, preprint, 2009, available online at www.arxiv.org under reference arXiv 0903.2721].
In [20], a channel sensing order for a multichannel CRN has been proposed in which the channels are sensed in descending order according to their achievable data rates, but with unknown free probabilities of the primary user channels.
Indeed, this framework allows to model basic variables as cumulative distribution functions, distribution-free probability boxes, possibility distributions or families of intervals provided by experts, while representing the dependence of the implied variables by means of copulas.
Stephenson et al. reported a 6-year post-SRT progression-free probability of 48%% in patients with a PSA <0.5 ng/ml compared with 40, 28, and 18%% in patients with PSA levels of 0.51 1 ng/ml, 1.01 1.5 ng/ml, and >1.5 ng/ml, respectively [9].
Such networks are easily generated in the computer by firs assigning to each gene gn its number of outputs ln, taken from a scale-free probability distribution Po(l) = Cl−γ, where C is the normalization constant and γ is the scale-free exponent.
The relapse-free probability curves indicated that the relapse rate increased significantly with upregulation of FABP5, HspB1, and MnSOD.
