395 records matched your query       

05514aam a2200517 i 4500
001 FF8A2D4E323411EC8B1165C359ECA4DB
003 SILO
005 20211021010114
008 210507t20202020riua     b    000 0 eng c
010    $a 2021016981
020    $a 1470442981
020    $a 9781470442989
035    $a (OCoLC)1243508905
040    $a LBSOR/DLC $b eng $e rda $c DLC $d YDX $d UIU $d PAU $d TXI $d OCLCF $d LWU $d UNBCA $d DLC $d OCLCO $d NUI $d UtOrBLW $d SILO
042    $a pcc
100 1  $a Male, Camille, $d 1984- $e author. $4 http://id.loc.gov/vocabulary/relators/aut $0 http://id.loc.gov/authorities/names/no2021058905
245 10 $a Traffic distributions and independence : $b permutation invariant random matrices and the three notions of independence / $c Camille Male.
264  1 $a Providence, RI : $b American Mathematical Society, $c [2020]
300    $a v, 88 pages : $b illustrations ; $c 26 cm.
340    $p illustration $2 rdaill $0 http://rdaregistry.info/termList/IllusContent/1014
490 1  $a Memoirs of the American Mathematical Society, $x 0065-9266 ; $v number 1300
500    $a "September 2020, volume 267, number 1300 (fourth of 7 numbers)."
504    $a Includes bibliographical references (pages 87-88).
505 0  $a Statement of the main theorem and applications -- Definition of asymptotic traffic independence -- Examples and applications for classical large matrices -- Algebraic traffic spaces -- Traffic independence and the three classical notions -- Limit theorems for independent traffics.
520    $a Voiculescu's notion of asymptotic free independence is known for a large class of random matrices including independent unitary invariant matrices. This notion is extended for independent random matrices invariant in law by conjugation by permutation matrices. This fact leads naturally to an extension of free probability, formalized under the notions of traffic probability. The author first establishes this construction for random matrices and then defines the traffic distribution of random matrices, which is richer than the $^*$-distribution of free probability. The knowledge of the individual traffic distributions of independent permutation invariant families of matrices is sufficient to compute the limiting distribution of the join family. Under a factorization assumption, the author calls traffic independence the asymptotic rule that plays the role of independence with respect to traffic distributions. Wigner matrices, Haar unitary matrices and uniform permutation matrices converge in traffic distributions, a fact which yields new results on the limiting $^*$-distributions of several matrices the author can construct from them. Then the author defines the abstract traffic spaces as non commutative probability spaces with more structure. She proves that at an algebraic level, traffic independence in some sense unifies the three canonical notions of tensor, free and Boolean independence. A central limiting theorem is stated in this context, interpolating between the tensor, free and Boolean central limit theorems.
650  0 $a Random matrices. $0 http://id.loc.gov/authorities/subjects/sh86001920
650  0 $a Independence (Mathematics) $0 http://id.loc.gov/authorities/subjects/sh85064829
650  0 $a Asymptotic distribution (Probability theory) $0 http://id.loc.gov/authorities/subjects/sh85009054
650  0 $a Limit theorems (Probability theory) $0 http://id.loc.gov/authorities/subjects/sh85077023
650  0 $a Selfadjoint operators. $0 http://id.loc.gov/authorities/subjects/sh85119806
650  7 $a Selfadjoint operators. $2 fast $0 http://id.worldcat.org/fast/1111947 $0 http://id.worldcat.org/fast/1111947
650  7 $a Limit theorems (Probability theory) $2 fast $0 http://id.worldcat.org/fast/998881 $0 http://id.worldcat.org/fast/998881
650  7 $a Independence (Mathematics) $2 fast $0 http://id.worldcat.org/fast/968877 $0 http://id.worldcat.org/fast/968877
650  7 $a Asymptotic distribution (Probability theory) $2 fast $0 http://id.worldcat.org/fast/819866 $0 http://id.worldcat.org/fast/819866
650  7 $a Random matrices. $2 fast $0 http://id.worldcat.org/fast/1089803 $0 http://id.worldcat.org/fast/1089803
650  7 $a Theory of distributions (Functional analysis) $2 fast $0 http://id.worldcat.org/fast/1149672 $0 http://id.worldcat.org/fast/1149672
650  7 $a Traffic flow $x Mathematical models. $2 fast $0 http://id.worldcat.org/fast/1154154 $0 http://id.worldcat.org/fast/1154154
650  7 $a Linear and multilinear algebra; matrix theory -- Special matrices -- Random matrices. $2 msc
650  7 $a Functional analysis {For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx} -- Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$-) algebras, etc.) [See also 22D25, 47Lxx. $2 msc
650  7 $a Probability theory and stochastic processes {For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX} -- Limit theorems [See also 28Dxx, 60B12] -- Central limit and other weak. $2 msc
650  7 $a Category theory; homological algebra {For commutative rings see 13Dxx, for associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and 55Uxx for. $2 msc
773 18 $w 990007620060202771 $g no:31858071393668
830  0 $a Memoirs of the American Mathematical Society ; $v no. 1300. $0 http://id.loc.gov/authorities/names/n83703151
941    $a 1
952    $l OVUX522 $d 20220317031308.0
956    $a http://locator.silo.lib.ia.us/search.cgi?index_0=id&term_0=FF8A2D4E323411EC8B1165C359ECA4DB