On the graphs and asymptotic forms of finite boolean relation matrices and stochastic matrices

1957 ◽  
Vol 4 (2) ◽  
pp. 151-167 ◽  
Author(s):  
David Rosenblatt
Keyword(s):  
Stochastic Matrices ◽  
Asymptotic Forms

Products of 2 × 2 stochastic matrices with random entries

1986 ◽  
Vol 23 (04) ◽  
pp. 1019-1024
Author(s):  
Walter Van Assche
Keyword(s):  
Rate Of Convergence ◽  
Beta Distribution ◽  
Stopping Time ◽  
Stochastic Matrices

The limit of a product of independent 2 × 2 stochastic matrices is given when the entries of the first column are independent and have the same symmetric beta distribution. The rate of convergence is considered by introducing a stopping time for which asymptotics are given.

scholarly journals A short note on extreme points of certain polytopes

2020 ◽  
Vol 8 (1) ◽  
pp. 36-39
Author(s):  
Lei Cao ◽  
Ariana Hall ◽  
Selcuk Koyuncu
Keyword(s):  
Short Proof ◽  
Convex Polytopes ◽  
Short Note ◽  
Convex Polytope ◽  
Extreme Points ◽  
Alternative Proof ◽  
Stochastic Matrices ◽  
Doubly Stochastic ◽  
Birkhoff's Theorem ◽  
Birkhoff’S Theorem

AbstractWe give a short proof of Mirsky’s result regarding the extreme points of the convex polytope of doubly substochastic matrices via Birkhoff’s Theorem and the doubly stochastic completion of doubly sub-stochastic matrices. In addition, we give an alternative proof of the extreme points of the convex polytopes of symmetric doubly substochastic matrices via its corresponding loopy graphs.

scholarly journals Positional Voting and Doubly Stochastic Matrices

2021 ◽  
Vol 128 (4) ◽  
pp. 337-351
Author(s):  
Jacqueline Anderson ◽  
Brian Camara ◽  
John Pike
Keyword(s):  
Stochastic Matrices ◽  
Doubly Stochastic ◽  
Doubly Stochastic Matrices ◽  
Positional Voting

Orthogonal cycle transforms of stochastic matrices

1997 ◽  
Vol 16 (3) ◽  
pp. 363-374 ◽  
Author(s):  
S. Kalpazidou ◽  
Joel E. Cohen
Keyword(s):  
Stochastic Matrices

scholarly journals Relative entropy under mappings by stochastic matrices

1993 ◽  
Vol 179 ◽  
pp. 211-235 ◽  
Author(s):  
Joel E. Cohen ◽  
Yoh Iwasa ◽  
Gh. Rautu ◽  
Mary Beth Ruskai ◽  
Eugene Seneta ◽  
...  
Keyword(s):  
Relative Entropy ◽  
Stochastic Matrices

scholarly journals Asymptotic expansions of Lambert series and related q-series

2017 ◽  
Vol 13 (08) ◽  
pp. 2097-2113 ◽  
Author(s):  
Shubho Banerjee ◽  
Blake Wilkerson
Keyword(s):  
Asymptotic Expansion ◽  
Asymptotic Expansions ◽  
Theta Functions ◽  
Lambert Series ◽  
Pochhammer Symbol ◽  
Complete Asymptotic Expansion ◽  
Polygamma Functions ◽  
Jacobi Theta Functions ◽  
Relative Errors ◽  
Asymptotic Forms

We study the Lambert series [Formula: see text], for all [Formula: see text]. We obtain the complete asymptotic expansion of [Formula: see text] near [Formula: see text]. Our analysis of the Lambert series yields the asymptotic forms for several related [Formula: see text]-series: the [Formula: see text]-gamma and [Formula: see text]-polygamma functions, the [Formula: see text]-Pochhammer symbol and the Jacobi theta functions. Some typical results include [Formula: see text] and [Formula: see text], with relative errors of order [Formula: see text] and [Formula: see text] respectively.

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