Distributions in free probability theory

[目次]

  • Contents / p1
  • Introduction / p2
  • 1.Free probability theory / p10
  • 1.1.Noncommutative probability space and freeness / p10
  • 1.2.Realization of semicircle law / p13
  • 1.3.Additive free convolution and R-transform / p16
  • 2.Random walk on free groups / p18
  • 2.1.Random walk / p18
  • 2.2.Random walk on free groups / p20
  • 2.3.Calculation of transition probabilities / p26
  • 3.The characterizations of a semicircle law / p30
  • 3.1.Freeness of the linear form and the quadratic form / p30
  • 3.2.Remaining free under rotations and semicircle laws / p35
  • 4.Free chi-square distribution / p44
  • 4.1.Symmetric quadratic forms in free random variables / p44
  • 4.2.Free chi-square distribution / p48
  • 5.A certain measure corresponding to random variables / p53
  • 5.1.Stieltjes inversion formula / p53
  • 5.2.Multiplicative free convolution and S-transform / p58
  • 5.3.Spectrum of random variable formed by two projections / p61
  • 5.4.Measure for a certain self-adjoint random variable / p69
  • 5.5.Brown measure / p74
  • Acknowledgement / p77
  • References / p78

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この本の情報

書名 Distributions in free probability theory
著作者等 樋渡 修
書名別名 自由確率論における分布について
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