Combinatorial properties of random graphs and matrices/ (Record no. 38717)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 02617n a2200301#a 4500 |
| 001 - CONTROL NUMBER | |
| control field | 40075 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | P5A |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20230123132000.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cuuuuuauuuu |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 210614s2021 bl por d |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | ocm51338542 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | P5A |
| Transcribing agency | P5A |
| 090 ## - IMPA CODE FOR CLASSIFICATION SHELVES | |
| IMPA CODE FOR CLASSIFICATION SHELVES | Teses do IMPA |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Mattos, Letícia Dias |
| 9 (RLIN) | 1184 |
| 245 10 - TITLE STATEMENT | |
| Title | Combinatorial properties of random graphs and matrices/ |
| Statement of responsibility, etc. | Letícia Dias Mattos. |
| 246 11 - VARYING FORM OF TITLE | |
| Title proper/short title | Propriedades combinatoriais de matrizes e gráficos aleatórios |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. | |
| Place of publication, distribution, etc. | Rio de Janeiro: |
| Name of publisher, distributor, etc. | IMPA, |
| Date of publication, distribution, etc. | 2021. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | video online |
| 500 ## - GENERAL NOTE | |
| General note | Defesa de Tese. |
| 500 ## - GENERAL NOTE | |
| General note | Banca examinadora: Robert Morris (IMPA, orientador) Roberto Imbuzeiro Oliveira (IMPA) Maurício Collares (UFMG) Taísa Martins (UFF) Guilherme Oliveira Mota (USP) Suplente: Simon Griffiths (PUC-Rio) |
| 505 1# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Abstract: In this thesis we study two of the main objects in probabilistic combinatorics: random matrices and random graphs. In the first part, joint with Campos, Morris and Morrison, we consider a uniformly-chosen random symmetric matrix with entries in {-1,+1}. We obtain an exponential-type bound on the probability that this matrix is singular. Our main new ingredient is an inverse Littlewood--Offord theorem whose statement is inspired by the method of hypergraph containers. In the second part, joint with Griffiths and Morris, we study the size of the maximum k-clique packing in the random graph G(n,p). A clique packing is just a set of edge-disjoint cliques. For every value of k which is close to the size of the largest clique in G(n,p), we obtain the order of the maximum k-clique packing in G(n,p). To show this result, we follow a random greedy process and use the differential equation method. In the third part, joint with Liebenau, Mendonça and Skokan, we study asymmetric Ramsey properties of G(n,p) for cliques and cycles. For any pair of r-clique and k-cycle, we determine the threshold for finding a red copy of a r-clique or a blue copy of a k-cycle in every red and blue edge-colouring of G(n,p). The main tool behind the proof is a structural characterisation of Ramsey graphs for each pair of r-clique and k-cycle . |
| 650 04 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Matematica. |
| Source of heading or term | larpcal |
| 9 (RLIN) | 19899 |
| 697 ## - LOCAL SUBJECT | |
| Local Subject | Teses do IMPA |
| Linkage | 24311 |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Morris, Robert, |
| Affiliation | (IMPA) |
| Relator term | orientador |
| 9 (RLIN) | 974 |
| 711 2# - ADDED ENTRY--MEETING NAME | |
| Meeting name or jurisdiction name as entry element | Defesa de Tese |
| 9 (RLIN) | 10070 |
| 856 4# - ELECTRONIC LOCATION AND ACCESS | |
| Public note | VIDEO |
| Uniform Resource Identifier | <a href="https://bit.ly/2TnAVEI">https://bit.ly/2TnAVEI</a> |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Source of classification or shelving scheme | Instituto de Matemática Pura e Aplicada |
| Koha item type | VIDEO |
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