scholarly journals Decompositions of stochastic processes based on irreducible group representations

2009 ◽  
Vol 54 (2) ◽  
pp. 304-336 ◽  
Author(s):  
Giovanni Peccati ◽  
Giovanni Peccati ◽  
Jean-Renaud Pycke ◽  
Jean-Renaud Pycke
Keyword(s):  
Stochastic Processes ◽  
Group Representations ◽  
Irreducible Group

THE SOLUTION OF THE THREE-DIMENSIONAL TWISTED GROUP LATTICES

1992 ◽  
Vol 06 (10) ◽  
pp. 1631-1645 ◽  
Author(s):  
STUART SAMUEL
Keyword(s):  
Partition Function ◽  
Statistical Mechanics ◽  
Three Dimensional ◽  
Group Representations ◽  
Screw Dislocations ◽  
Irreducible Group ◽  
Twisted Group ◽  
Free Propagation

We define new lattices called d-dimensional twisted group lattices. They are similar to ordinary lattices except that abstract screw dislocations are present at the centers of all plaquettes. Some physical aspects are enumerated. We consider the statistical mechanics system of free propagation on the three-dimensional twisted group lattice. For this case, the partition function is explicitly computed by finding the irreducible group representations.

On group representations and invariant stochastic processes

1963 ◽  
Vol 59 (2) ◽  
pp. 431-450 ◽  
Author(s):  
A. D. Mclaren
Keyword(s):  
Finite Number ◽  
Stochastic Processes ◽  
Group Representations

AbstractThe theory of group representations is explored with regard to statistical applications. Ease of analysis depends rather critically on the amount of symmetry present and this point is examined in detail. ‘ Stationarity’ assumptions are considered for a finite number of variates, with examples of their use in experimental situations.

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