Diffusive clustering:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
1996
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 102 S. Ill., graph. Darst. |
Staff View
MARC
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| 100 | 1 | |a Klenke, Achim |e Verfasser |0 (DE-588)1036340058 |4 aut | |
| 245 | 1 | 0 | |a Diffusive clustering |c vorgelegt von Achim Klenke |
| 264 | 1 | |c 1996 | |
| 300 | |a 102 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |a Erlangen-Nürnberg, Univ., Diss., 1996 | ||
| 650 | 0 | 7 | |a Cluster |0 (DE-588)4010318-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Zufälliges dynamisches System |0 (DE-588)4335207-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Diffusion |0 (DE-588)4012277-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Teilchenmodell |0 (DE-588)4128081-7 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1807320565578465280 |
|---|---|
| adam_text |
CONTENTS
PART
I,
INTRODUCTION
TO
QUESTIONS
CONCERNING
THE
LONG-TIME
BEHAVIOUR
OF
INTERACTING
SYSTEMS
3
PREFACE
.
3
1
THE
MODELS
.
4
1.1
BRANCHING
MODELS
.
4
1.2
VOTER
MODEL
.
4
1.3
INTERACTING
DIFFUSIONS
.
5
2
BASIC
ERGODIC
THEORY
.
6
3
DIFFUSIVE
CLUSTERING
.
8
3.1
CONCEPTS
OF
CLUSTERING
.
8
3.2
DIFFUSIVE
CLUSTERING
FOR
THE
VOTER
MODEL
.
10
3.3
DIFFUSIVE
CLUSTERING
FOR
THE
HIERARCHICAL
GROUP
.
12
3.4
BRANCHING
MODELS
.
14
4
FINITE
SYSTEMS
.
16
4.1
MOTIVATION
.
16
4.2
CONCEPTS,
HISTORY
OF
THE
SUBJECT
.
16
4.3
INTERACTING
DIFFUSIONS
.
16
4.4
BRANCHING
MODELS
.
19
PART
II,
HIERARCHICALLY
INTERACTING
DIFFUSIONS
21
1
INTRODUCTION
AND
MAIN
RESULTS
.
22
1.1
SURVEY
.
22
1.2
INTRODUCTION
.
22
1.3
CLUSTERING
IN
INFINITE
SYSTEMS
.
23
1.4
FINITE
SYSTEMS
VERSUS
INFINITE
SYSTEMS
.
28
1.5
OUTLINE
.
30
2
RANDOM
WALK
ESTIMATES
.
31
2.1
PREPARATIONS
.
31
2.2
SCALED
LIMITS
OF
HITTING
TIMES
.
32
2.3
APPLICATION
TO
.
34
2.4
APPLICATION
TO
E
.
35
3
COALESCING
RANDOM
WALKS
.
40
3.1
PREPARATIONS
.
40
3.2
SCALING
PROPERTIES
OF
IJ(T)
ON
E
.
41
3.3
SCALING
PROPERTIES
OF
FJ
N
(T)
ON
E
N
.
43
3.4
CASE
A
RECURRENT,
COMPARISON
OF
R](T)
AND
TJ(T)
.
44
3.5
CASE
A
TRANSIENT,
COMPARISON
OF
R)(T)
AND
RIN(T)
.
45
2
CONTENTS
4
PROOF
OF
THEOREM
1,3
AND
4
.
46
4.1
PROOF
OF
THEOREM
1
AND
4
.
46
4.2
PROOF
OF
THEOREM
3
.
49
5
PROOF
OF
THEOREM
2
AND
5
.
49
5.1
LIMIT
PROCESS
OF
SCALED
RANDOM
WALKS
.
50
5.2
PROOF
OF
THEOREMS
2
AND
5,
PART
A)
.
51
5.3
PROOF
THEOREMS
2
AND
5,
PART
B)
.
52
5.4
PROOF
THEOREMS
2
AND
5,
PART
C)
.
53
6
THE
BEHAVIOUR
OF
THE
OCCUPATION
TIMES
.
56
PART
III,
THE
BRANCHING
MODELS
63
1
INTRODUCTION
.
64
1.1
BACKGROUND
.
64
1.2
THE
MODELS
.
65
1.3
BASIC
ERGODIC
THEORY
.
67
2
RESULTS
.
67
2.1
CLUSTER
FORMATION
FOR
D
=
2
.
67
2.2
FINITE
SYSTEMS,
STABLE
CASE
.
72
2.3
FINITE
SYSTEMS,
CRITICAL
DIMENSION
.
73
2.4
OUTLINE
.
74
3
BASIC
TOOLS
.
74
3.1
MOMENT
FORMULAS
.
75
3.2
COUPLING
.
77
3.3
COMPARISON
.
82
4
MOMENT
CALCULATIONS
IN
THE
CRITICAL
DIMENSION
.
83
5
PROOF
OF
THE
CLUSTERING
RESULTS
FOR
THE
INFINITE
SYSTEMS
.
91
5.1
PROOF
OF
THEOREM
1
.
91
5.2
PROOF
OF
THEOREM
2
.
93
6
PROOFS
FOR
FINITE
SYSTEMS
.
95
6.1
PROOF
OF
THEOREM
3
.
95
6.2
PROOF
OF
THEOREM
4
AND
5
.
96
APPENDIX
97
1
DESCRIPTION
OF
THE
SIMULATIONS
.
97
REFERENCES
99 |
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| author | Klenke, Achim |
| author_GND | (DE-588)1036340058 |
| author_facet | Klenke, Achim |
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| author_variant | a k ak |
| building | Verbundindex |
| bvnumber | BV010699233 |
| classification_tum | MAT 602d PHY 015d |
| ctrlnum | (OCoLC)258213247 (DE-599)BVBBV010699233 |
| discipline | Physik Mathematik |
| format | Thesis Book |
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV010699233 |
| illustrated | Illustrated |
| indexdate | 2024-08-14T00:26:44Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007141129 |
| oclc_num | 258213247 |
| open_access_boolean | |
| owner | DE-29 DE-29T DE-91 DE-BY-TUM DE-355 DE-BY-UBR DE-12 DE-703 DE-11 DE-188 |
| owner_facet | DE-29 DE-29T DE-91 DE-BY-TUM DE-355 DE-BY-UBR DE-12 DE-703 DE-11 DE-188 |
| physical | 102 S. Ill., graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| record_format | marc |
| spelling | Klenke, Achim Verfasser (DE-588)1036340058 aut Diffusive clustering vorgelegt von Achim Klenke 1996 102 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Erlangen-Nürnberg, Univ., Diss., 1996 Cluster (DE-588)4010318-3 gnd rswk-swf Zufälliges dynamisches System (DE-588)4335207-8 gnd rswk-swf Diffusion (DE-588)4012277-3 gnd rswk-swf Teilchenmodell (DE-588)4128081-7 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Cluster (DE-588)4010318-3 s Diffusion (DE-588)4012277-3 s DE-604 Teilchenmodell (DE-588)4128081-7 s Zufälliges dynamisches System (DE-588)4335207-8 s DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007141129&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Klenke, Achim Diffusive clustering Cluster (DE-588)4010318-3 gnd Zufälliges dynamisches System (DE-588)4335207-8 gnd Diffusion (DE-588)4012277-3 gnd Teilchenmodell (DE-588)4128081-7 gnd |
| subject_GND | (DE-588)4010318-3 (DE-588)4335207-8 (DE-588)4012277-3 (DE-588)4128081-7 (DE-588)4113937-9 |
| title | Diffusive clustering |
| title_auth | Diffusive clustering |
| title_exact_search | Diffusive clustering |
| title_full | Diffusive clustering vorgelegt von Achim Klenke |
| title_fullStr | Diffusive clustering vorgelegt von Achim Klenke |
| title_full_unstemmed | Diffusive clustering vorgelegt von Achim Klenke |
| title_short | Diffusive clustering |
| title_sort | diffusive clustering |
| topic | Cluster (DE-588)4010318-3 gnd Zufälliges dynamisches System (DE-588)4335207-8 gnd Diffusion (DE-588)4012277-3 gnd Teilchenmodell (DE-588)4128081-7 gnd |
| topic_facet | Cluster Zufälliges dynamisches System Diffusion Teilchenmodell Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007141129&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT klenkeachim diffusiveclustering |