A NEW PROOF OF FRIEDMAN'S SECOND EIGENVALUE THEOREM AND ITS EXTENSION TO RANDOM LIFTS

Charles BORDENAVE

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A NEW PROOF OF FRIEDMAN'S SECOND EIGENVALUE THEOREM AND ITS EXTENSION TO RANDOM LIFTS

机译：弗里德曼第二个特征值定理的新证明及其对随机升降机的延伸

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摘要

It was conjectured by Alon and proved by Friedman that a random d-regular graph has nearly the largest possible spectral gap, or, more precisely, that the largest absolute value of the nontrivial eigenvalues of its adjacency matrix is at most 2√d-1 + o(l) with probability tending to one as the size of the graph tends to infinity. We give a new proof of this statement. We also study related questions on random n -lifts of graphs and improve a recent result by Friedman and Kohler.

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来源
《Annales scientifiques de l'Ecole normale superieure》 |2020年第6期|共47页
作者
Charles BORDENAVE;
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作者单位

Institut de Mathématiques de Marseille CNRS and Aix-Marseille University 39 rue F. Joliot Curie 13453 Marseille Cedex 13 France;

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原文格式 PDF
正文语种 eng
中图分类自然科学总论;师范教育理论;
关键词
FRIEDMAN'S SECOND EIGENVALUE; RANDOM LIFTS; largest possible spectral gap;

机译：弗里德曼的第二个特征值;随机升降机;最大可能的光谱间隙;

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A NEW PROOF OF FRIEDMAN'S SECOND EIGENVALUE THEOREM AND ITS EXTENSION TO RANDOM LIFTS

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