General Lemmas on large deviations for a random vector with regular behavior of semiinvariants. III

1988 ◽  
Vol 28 (1) ◽  
pp. 58-66
Author(s):  
L. Saulis
Keyword(s):  
Large Deviations ◽  
Random Vector ◽  
Regular Behavior

The probabilities of large deviations for a certain class of statistics associated with multinomial distribution

2020 ◽  
Vol 24 ◽  
pp. 581-606
Author(s):  
Sherzod M. Mirakhmedov
Keyword(s):  
Large Deviations ◽  
Random Vector ◽  
Large Deviation ◽  
Multinomial Distribution ◽  
Negative Integer ◽  
Probabilities Of Large Deviations ◽  
Divergence Statistics ◽  
Power Divergence

Let η = (η1, …, ηN) be a multinomial random vector with parameters n = η1 + ⋯ + ηN and pm > 0, m = 1, …, N, p1 + ⋯ + pN = 1. We assume that N →∞ and maxpm → 0 as n →∞. The probabilities of large deviations for statistics of the form h1(η1) + ⋯ + hN(ηN) are studied, where hm(x) is a real-valued function of a non-negative integer-valued argument. The new large deviation results for the power-divergence statistics and its most popular special variants, as well as for several count statistics are derived as consequences of the general theorems.

Association Model for Liquid Alloys

1982 ◽  
Vol 19 ◽  
Author(s):  
Ferdinand Sommer
Keyword(s):  
Large Deviations ◽  
Temperature Dependence ◽  
Physical Significance ◽  
Liquid Alloys ◽  
Association Model ◽  
Compound Formation ◽  
Regular Behavior ◽  
Good Accordance ◽  
Experimental Values ◽  
Miscibility Gaps

ABSTRACTThe concentration and the temperature dependence of thermodynamic mixing functions of liquid alloys with compound formation tendency, which often exhibit large deviations from a regular behavior, can be calculated according to an association model using only a few parameters which have a definite physical significance. The results obtained for binary and ternary alloy melts with one ore more, simultaneously occurring, binary or ternary associates are in good accordance with the experimental values. For the calculation of phase diagrams, the association model enables a correct extrapolation into concentration and temperature regions for which no experimental results are available. The occurrence and the borderline of miscibility gaps in liquid alloys with strong compound forming tendency can be quantitatively described.

scholarly journals Run-and-Tumble Motion: The Role of Reversibility

2021 ◽  
Vol 183 (3) ◽  
Author(s):  
Bart van Ginkel ◽  
Bart van Gisbergen ◽  
Frank Redig
Keyword(s):  
Free Energy ◽  
Diffusion Coefficient ◽  
Large Deviations ◽  
Energy Function ◽  
Internal State ◽  
Rate Function ◽  
Free Energy Function ◽  
Large Deviations Principle ◽  
Preferred Direction ◽  
State Process

AbstractWe study a model of active particles that perform a simple random walk and on top of that have a preferred direction determined by an internal state which is modelled by a stationary Markov process. First we calculate the limiting diffusion coefficient. Then we show that the ‘active part’ of the diffusion coefficient is in some sense maximal for reversible state processes. Further, we obtain a large deviations principle for the active particle in terms of the large deviations rate function of the empirical process corresponding to the state process. Again we show that the rate function and free energy function are (pointwise) optimal for reversible state processes. Finally, we show that in the case with two states, the Fourier–Laplace transform of the distribution, the moment generating function and the free energy function can be computed explicitly. Along the way we provide several examples.

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