The asymmetric continuous distribution function of the effective field of the Ising model in the spin glass and the ferromagnetic states on the Bethe lattice

1989 ◽  
Vol 157 (3) ◽  
pp. 1195-1202 ◽  
Author(s):  
Mitsuhiro Sasaki ◽  
Shigetoshi Katsura
Keyword(s):  
Distribution Function ◽  
Ising Model ◽  
Spin Glass ◽  
Continuous Distribution ◽  
Bethe Lattice ◽  
Effective Field ◽  
Continuous Distribution Function

New method for the restoration of the continuous distribution function of hyperfine fields andits possibilities

1993 ◽  
Vol 78 (1-4) ◽  
pp. 391-396 ◽  
Author(s):  
S. D. Antipov ◽  
G. E. Gorjunov ◽  
A. F. Djura ◽  
Ju. M. Polukarov ◽  
D. V. Sadkov ◽  
...  
Keyword(s):  
Distribution Function ◽  
Continuous Distribution ◽  
New Method ◽  
Continuous Distribution Function ◽  
Hyperfine Fields

Records from a power model of independent observations

1995 ◽  
Vol 32 (4) ◽  
pp. 982-990 ◽  
Author(s):  
Ishay Weissman
Keyword(s):  
Distribution Function ◽  
Wide Spectrum ◽  
Continuous Distribution ◽  
Random Variables ◽  
Continuous Distribution Function ◽  
Power Model ◽  
Record Times ◽  
Independent Sequence ◽  
Independent Observations

Records from are analyzed, where {Yj} is an independent sequence of random variables. Each Yj has a continuous distribution function Fj = Fλj for some distribution F and some λ j > 0. We study records, record times and related quantities for this sequence. Depending on the sequence of powers , a wide spectrum of behaviour is exhibited.

On the law of the iterated logarithm for inter-record times

1970 ◽  
Vol 7 (02) ◽  
pp. 432-439 ◽  
Author(s):  
William E. Strawderman ◽  
Paul T. Holmes
Keyword(s):  
Distribution Function ◽  
Probability Space ◽  
Continuous Distribution ◽  
Random Variables ◽  
Continuous Distribution Function ◽  
Record Times ◽  
Iterated Logarithm ◽  
The Law ◽  
Image Position ◽  
Independent Identically Distributed

Let X 1, X2, X 3 , ··· be independent, identically distributed random variables on a probability space (Ω, F, P); and with a continuous distribution function. Let the sequence of indices {Vr } be defined as Also define The following theorem is due to Renyi [5].

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