scholarly journals On the Degree of the GCD of Random Polynomials over a Finite Field

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Kui Liu ◽  
Meijie Lu
Keyword(s):  
Probability Distribution ◽  
Finite Field ◽  
Waiting Time ◽  
Greatest Common Divisor ◽  
Random Polynomials ◽  
Fixed Degree

In this paper, we focus on the degree of the greatest common divisor ( gcd ) of random polynomials over F q . Here, F q is the finite field with q elements. Firstly, we compute the probability distribution of the degree of the gcd of random and monic polynomials with fixed degree over F q . Then, we consider the waiting time of the sequence of the degree of gcd functions. We compute its probability distribution, expectation, and variance. Finally, by considering the degree of a certain type gcd , we investigate the probability distribution of the number of rational (i.e., in F q ) roots (counted with multiplicity) of random and monic polynomials with fixed degree over F q .

Random Dieudonné modules, random -divisible groups, and random curves over finite fields

2013 ◽  
Vol 12 (3) ◽  
pp. 651-676 ◽  
Author(s):  
Bryden Cais ◽  
Jordan S. Ellenberg ◽  
David Zureick-Brown
Keyword(s):  
Probability Distribution ◽  
Finite Field ◽  
Random Matrix ◽  
Hyperelliptic Curve ◽  
Hyperelliptic Curves ◽  
Plane Curves ◽  
Random Curves ◽  
Isomorphism Classes ◽  
Curves Over Finite Fields ◽  
Divisible Groups

AbstractWe describe a probability distribution on isomorphism classes of principally quasi-polarized $p$-divisible groups over a finite field $k$ of characteristic $p$ which can reasonably be thought of as a ‘uniform distribution’, and we compute the distribution of various statistics ($p$-corank, $a$-number, etc.) of $p$-divisible groups drawn from this distribution. It is then natural to ask to what extent the $p$-divisible groups attached to a randomly chosen hyperelliptic curve (respectively, curve; respectively, abelian variety) over $k$ are uniformly distributed in this sense. This heuristic is analogous to conjectures of Cohen–Lenstra type for $\text{char~} k\not = p$, in which case the random $p$-divisible group is defined by a random matrix recording the action of Frobenius. Extensive numerical investigation reveals some cases of agreement with the heuristic and some interesting discrepancies. For example, plane curves over ${\mathbf{F} }_{3} $ appear substantially less likely to be ordinary than hyperelliptic curves over ${\mathbf{F} }_{3} $.

Roots of random polynomials over a finite field

2006 ◽  
Vol 80 (1-2) ◽  
pp. 300-304 ◽  
Author(s):  
V. K. Leont’ev
Keyword(s):  
Finite Field ◽  
Random Polynomials

Zeros of random polynomials over finite fields

1992 ◽  
Vol 111 (2) ◽  
pp. 193-197 ◽  
Author(s):  
R. W. K. Odoni
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Prime Power ◽  
Random Polynomials ◽  
Polynomials Over Finite Fields ◽  
Image Position

Let be the finite field with q elements (q a prime power), let r 1 and let X1, , Xr be independent indeterminates over . We choose an arbitrary and a d 1 and consider

scholarly journals A note on M/G/1 vacation systems with waiting time limits

1990 ◽  
Vol 22 (2) ◽  
pp. 513-518 ◽  
Author(s):  
T. Takine ◽  
T. Hasegawa
Keyword(s):  
Probability Distribution ◽  
Residence Time ◽  
Waiting Time ◽  
Waiting Times ◽  
Distribution Functions ◽  
Multiple Vacations ◽  
Time Limits ◽  
Probability Distribution Functions ◽  
Two Systems

We consider two variants of M/G/1 queues with exhaustive service and multiple vacations; (1) customers cannot wait for their services longer than an interval of length T, and (2) customers cannot stay in the system longer than an interval of length T. We show that the probability distribution functions of the waiting times for the two systems are given in terms of those for the corresponding M/G/1 vacation systems without any residence-time limits.

scholarly journals MENENTUKAN METODE INPUT PROBABILITY DISTRIBUTION DALAM PEMODELAN DAN SIMULASI DI ANTRIAN KASIR TOKO BUKU PT. XYZ

Jurnal PASTI ◽  
2020 ◽  
Vol 13 (3) ◽  
pp. 250
Author(s):  
Mega Purnamasari ◽  
Titi Iswari ◽  
Frylie Frescia Falen
Keyword(s):  
Probability Distribution ◽  
Waiting Time ◽  
Input Probability

PT XYZ merupakan perusahaan yang memiliki banyak toko penjualan buku yang tersebar di Indonesia. PT XYZ berusaha melakukan perbaikan yang berkesinambungan dalam melakukan pelayanan terhadap pelanggan salah satunya adalah antrian di kasir. Sistem dapat diperbaiki dengan cara membuat skenario-skenario yang kemudian dilakukan pemodelan dan simulasi. Kita harus bisa memilih metode pemodelan dan simulasi yang terbaik yang memiliki dampak error terkecil. Memodelkan dan simulasi sistem nyata dapat dilakukan dengan beberapa pendekatan dalam input probability distribution antara lain metode trace driven, metode empris, dan metode teoritis. Pada penelitian ini dilakukan pemodelan dan simulasi di antrian kasir di PT XYZ dengan menggunakan ketiga metode pendekatan tersebut. Dari ketiga hasil simulasi didapatkan bahwa semua hasil waiting time dari ketiga metode tidak memiliki perbedaan yang berarti antara data sistem nyata dengan model sistem nyata. Kemudian dari selisih total waiting time, utilisasi, dan jumlah pelanggan yang terlayani metode trace driven adalah metode terbaik.

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