Mešanje z naključnimi transpozicijami

delo diplomskega seminarja

Matevž Miščič (Author), Urban Jezernik (Mentor)

Abstract

V diplomski nalogi dokažemo, da pri mešanju z naključnimi transpozicijami pride do odreza ob času $\frac{1}{2}n\log{n}$. Pri dokazu zgornje meje odreza uporabimo nekomutativno Fourierovo transformacijo, za njeno uporabo pa predstavimo teorijo upodobitev končnih grup s posebnim poudarkom na simetrične grupe. Klasificiramo Spechtove module in pokažemo, da standardni politabloidi tvorijo njihove baze. Spodnjo mejo odreza dokažemo z verjetnostnimi metodami. Predstavimo tudi nekaj nadaljnjih primerov odreza pri sprehodih po grupah.

Keywords

matematika;upodobitve grup;simetrične grupe;naključni sprehodi;naključne transpozicije;

Data

Language:	Slovenian
Year of publishing:	2022
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[M. Miščič]
UDC:	512
COBISS:	120837379
Views:	593
Downloads:	133
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Shuffling by random transpositions
Secondary abstract:	In this thesis we prove that in the case of random transposition shuffling cutoff occurs at time $\frac{1}{2}n\log{n}$. The upper bound is proved using noncommutative Fourier transform. To understand it representation theory of finite groups is presented with emphasis on symmetric groups. Specht modules are classified and it is shown that standard polytabloids form their bases. Lower bound is proved using methods from probability. We also discuss some further examples of cutoff for random walks on groups.
Secondary keywords:	mathematics;group representations;symmetric groups;random walks;random transpositions;
Type (COBISS):	Final seminar paper
Study programme:	0
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages:	37 str.
ID:	16400972