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The "stochastic" part is because there is also a small probability of random star formation in all areas in the disk which keeps things going.
The EBSD observation of the specimen showed an increase in the frequency of coincident site lattice (CSL) boundaries and a decrease in the percolation probability of random boundaries.
Based on that two stochastic micro-mechanic models are presented that can predict with confidence the failure probability of random matrix inclusion composites.
A CSL frequency of over 82% may result in a very low percolation probability of random boundary networks in per-threshold and a remarkable suppression of intergranular deterioration during twin-induced grain boundary engineering of austenitic stainless steels.
This model has recently been justified on the basis of the probability of random jumps of atomic lattice cracks over the activation energy barriers on the free energy potential of the lattice.
In particular, we make a critical use of the structure theorem from [Terence Tao, Van Vu, On the singularity probability of random Bernoulli matrices, J. Amer. Math. Soc. 20 (2007) 603 628], which was obtained using tools from additive combinatorics.
Most notably, the time required to perform an assay to an equivalent assay mass variance is greatly reduced with a fast-neutron system, by more than an order of magnitude compared with that of the thermal-neutron system, due to the reduced probability of random summing with the fast system.
Our method is a refinement of those from [Jeff Kahn, János Komlós, Endre Szemerédi, On the probability that a random ±1-matrix is singular, J. Amer. Math. Soc. 8 (19951995) 223 240; Terence Tao, Van Vu, On the singularity probability of random Bernoulli matrices, J. Amer. Math. Soc. 20 (2007) 603 628].
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They had five options to choose from: very low probability, low probability, sort of random, high probability, and very high probability.
His group did much of the research that led to postal systems that can recognize handwritten addresses on envelopes, and he works with databases of fingerprints to derive probabilities of random correspondence between two prints.
Sections 5.2 and 5.3 deal with applications of the presented geometric and stochastic representations to simulating probabilities of random events and to linear transformations, respectively.
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