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Weak Compactness of Random Sumsof Independent Random Variables
Theory of Probability & Its Applications, 1999Summary: The shift-compactness of random sums \(S_{N_n}^{(n)}\), \(S_k^{(n)}=X_{n,1}+\cdots +X_{n,k}\), of independent random variables is investigated under the assumptions that in each sum the summands and their number \(N_n\) are independent and that the summands satisfy the condition of uniform asymptotic negligibility in the form \(\max_{1\leq k ...
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The Power and Weakness of Randomness in Computation
2006Humanity has grappled with the meaning and utility of randomness for centuries. Research in the Theory of Computation in the last thirty years has enriched this study considerably. We describe two main aspects of this research on randomness, demonstrating its power and weakness respectively.
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Weak Mixing of Random Walks on Groups
Journal of Theoretical Probability, 2003Let \(\mu\) be a probability measure on a locally compact \(\sigma\)-compact group. The authors prove that a random walk associated with \(\mu\) is weakly mixing if and only if it is ergodic and strictly aperiodic. The proof is based on results on the eigenvalues of the associated transition operators.
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Random variables in weak typep spaces
Archiv der Mathematik, 1992Although weak type \(p\) spaces are introduced by geometric properties a characterization by the behaviour of random variables with values in these spaces is given which corresponds to the properties of type \(p\) spaces.
Defant, Martin, Junge, Marius
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Security Weaknesses in a Randomized Stream Cipher
2000TriStrata appears to have implemented a variation of Maurer’s randomised cipher. We define a variation of Maurer’s cipher that appears to be similar to the TriStrata version, and show several cryptanalytical attacks against our variant.
Niels Ferguson +2 more
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On weak convergence of random fields
Annals of the Institute of Statistical Mathematics, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Davydov, Youri, Zitikis, Ričardas
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On weak convergence of random fields
Lithuanian Mathematical Journal, 1999A criterion of compactness is established for sets in the space \(D\) introduced by the authors [ibid. 30, No. 3, 195-208 (1990), resp. ibid. 30, No. 3, 453-469 (1990; Zbl 0722.60012)]. This \(D\) consisting of functions on \([0,1]^2\) whose discontinuity points lie on smooth curves is viewed with metric making it a Polish space.
Banys, R., Surgailis, D.
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Extractors for weak random sources and their applications
1998An extractor is an algorithm which, on input a long string from a defective random source and a short truly random string, outputs a long almost-random string. In this talk, we survey extractors for weak random sources and their applications.
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WEAK UNCORRELATEDNESS OF RANDOM VARIABLES
Acta Mathematica Scientia, 2006Abstract New measures of independence for n random variables, based on their moments, are studied. A scale of degrees of independence for random variables which starts with uncorrelatedness (for n = 2) and finishes at independence is constructed. The scale provides a countable linearly ordered set of measures of independence.
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