Generalized semistable probability distributions in Hilbert space

1980 ◽  
Vol 20 (2) ◽  
pp. 111-118 ◽  
Author(s):  
D. Krapavickaitė
Keyword(s):  
Hilbert Space ◽  
Probability Distributions ◽  
Semistable Probability

scholarly journals Operator semistable probability measures on a Hilbert space: Corrigenda

1980 ◽  
Vol 22 (3) ◽  
pp. 479-480
Author(s):  
R.G. Laha ◽  
V.K. Rohatgi
Keyword(s):  
Hilbert Space ◽  
Probability Measures ◽  
Semistable Probability

A faulty typescript of [2] was, regrettably, submitted. The following changes should be made:Page 398, line 7: replace A є G with A є L.Page 398, line 12: replace A є G with A є L.

scholarly journals Operator semistable probability measures on a Hilbert space

1980 ◽  
Vol 22 (3) ◽  
pp. 397-406 ◽  
Author(s):  
R.G. Laha ◽  
V.K. Rohatgi
Keyword(s):  
Hilbert Space ◽  
Separable Hilbert Space ◽  
Probability Measures ◽  
Real Separable Hilbert Space ◽  
Semistable Probability

A characterization of the class of operator semistable probability measures on a real separable Hilbert space is given.

scholarly journals Finite-Size Scaling of Typicality-Based Estimates

2020 ◽  
Vol 75 (5) ◽  
pp. 465-473 ◽  
Author(s):  
Jürgen Schnack ◽  
Johannes Richter ◽  
Tjark Heitmann ◽  
Jonas Richter ◽  
Robin Steinigeweg
Keyword(s):  
Hilbert Space ◽  
Standard Deviation ◽  
Random Vector ◽  
Probability Distributions ◽  
Finite Size ◽  
System Size ◽  
Thermodynamic Quantities ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Full Temperature

AbstractAccording to the concept of typicality, an ensemble average can be accurately approximated by an expectation value with respect to a single pure state drawn at random from a high-dimensional Hilbert space. This random-vector approximation, or trace estimator, provides a powerful approach to, e.g. thermodynamic quantities for systems with large Hilbert-space sizes, which usually cannot be treated exactly, analytically or numerically. Here, we discuss the finite-size scaling of the accuracy of such trace estimators from two perspectives. First, we study the full probability distribution of random-vector expectation values and, second, the full temperature dependence of the standard deviation. With the help of numerical examples, we find pronounced Gaussian probability distributions and the expected decrease of the standard deviation with system size, at least above certain system-specific temperatures. Below and in particular for temperatures smaller than the excitation gap, simple rules are not available.

Asteroid and Comet Impact Speeds upon Mars: Significance for Panspermia and the Supply of Organics

1997 ◽  
Vol 161 ◽  
pp. 197-201 ◽  
Author(s):  
Duncan Steel
Keyword(s):  
Probability Distributions ◽  
Regions Of Interest ◽  
Significant Fraction ◽  
Organic Chemicals ◽  
Impact Speed ◽  
The Mean ◽  
The Impact

AbstractWhilst lithopanspermia depends upon massive impacts occurring at a speed above some limit, the intact delivery of organic chemicals or other volatiles to a planet requires the impact speed to be below some other limit such that a significant fraction of that material escapes destruction. Thus the two opposite ends of the impact speed distributions are the regions of interest in the bioastronomical context, whereas much modelling work on impacts delivers, or makes use of, only the mean speed. Here the probability distributions of impact speeds upon Mars are calculated for (i) the orbital distribution of known asteroids; and (ii) the expected distribution of near-parabolic cometary orbits. It is found that cometary impacts are far more likely to eject rocks from Mars (over 99 percent of the cometary impacts are at speeds above 20 km/sec, but at most 5 percent of the asteroidal impacts); paradoxically, the objects impacting at speeds low enough to make organic/volatile survival possible (the asteroids) are those which are depleted in such species.

Hilbert Space

1993 ◽  
Author(s):  
J. R. Retherford
Keyword(s):  
Hilbert Space
Sign in / Sign up

Export Citation Format

Share Document