2024/02/25 by Forrester, Peter J., Kumar, Santosh · 1 citation
#11B37 #15A18 #15B52 #33C45 #60B20 #62B10 #81P40 #Computation (stat.CO) #Data Analysis #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Probability (math.PR) #Statistics and Probability (physics.data-an)
paper · doi:10.48550/arxiv.2402.16069
We consider the problem of the exact computation of the marginal eigenvalue distributions in the Laguerre and Jacobi β ensembles. In the case β=1 this is a question of long standing in the mathematical statistics literature. A recursive procedure to accomplish this task is given for β a positive integer, and the parameter λ1 a non-negative integer. This case is special due to a finite basis of elementary functions, with coefficients which are polynomials. In the Laguerre case with β= 1 and λ1 + 1/2 a non-negative integer some evidence is given of their again being a finite basis, now consisting of elementary functions and the error function multiplied by elementary functions. Moreover, from this the corresponding distributions in the fixed trace case permit a finite basis of power functions, as also for λ1 a non-negative integer. The fixed trace case in this setting is relevant to quantum information theory and quantum transport problem, allowing particularly the exact determination of Landauer conductance distributions in a previously intractable parameter regime. Our findings also aid in analyzing zeros of the generating function for specific gap probabilities, supporting the validity of an associated large N local central limit theorem.