# Global multiplicity bounds and spectral statistics for random operators

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9,647 citations

### "Global multiplicity bounds and spec..." refers background or methods in this paper

...In the mid-fifties Anderson [1] proposed that for large disorder the models on l(Z) should exhibit localization....

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...In case of −∆, another method is to use smooth basis from L([0, 1]) and translate them using Z action to get the desired result....

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...d random variables following uniform distribution on [0, 1]....

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731 citations

### "Global multiplicity bounds and spec..." refers methods in this paper

...Several rigorous results on localization followed from the early eighties starting with the work of Fröhlich-Spencer [2] who formulated multi scale analysis....

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701 citations

### "Global multiplicity bounds and spec..." refers background in this paper

...There are several papers on local spectral statistics on discrete models such as [4, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45]....

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...Some of the papers on localization for large disorder are [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13] and [14, 15, 16, 17]....

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400 citations

### "Global multiplicity bounds and spec..." refers background in this paper

...Some of the papers on localization for large disorder are [2], [44], [19], [16] [23], [13, 14], [1], [30] and [11] and [9]....

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358 citations

### "Global multiplicity bounds and spec..." refers methods in this paper

...localization followed from the early eighties starting with the work of Frohlich-Spencer [20] who formulated multi scale analysis. Some of the papers on localization for large disorder are [2], [44], [19], [16] [23], [13, 14], [1], [30] and [11] and [9]. We refer to any of [10], [18], [29], [45] and [4]. The next set ofquestions concern thesimplicity ofthe Lebesgue components of spectrum and in this d...

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