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=10 ( * o' N) _ ' _ ' WIGNER SEMI_CIRCLF' q"()". ' - PDF document

Apr 03, 2024 •532 likes •609 views

qlFF, ln- I<?r)'h Iz f, =10 ( * o' N) _ ' _ ' WIGNER SEMI_CIRCLF' q"()". ' : : E r r ' r . ' pe-+. -r i-- " h: i- .fi-" of the aver- form the seml-cire'ular line sl*ows FIG. 1: The dashed its

  1. qlFF, ln- I<?r)'h Iz f, =10 ( * o' N) _ ' _ ' WIGNER SEMI_CIRCLF' q"()". ' : : E r r ' r . ' pe-+. -r i-- " h: i- .fi-" of the aver- form the seml-cire'ular line sl*ows FIG. 1: The dashed its around is centered The'l$g*g$&gtr$eqv+Lre dengllof state.s. age proba- l[-116' The *rd ffect*a&$ffith ff$o@r *,za,r by the Tracy-Widom s6{e ,i's,t*e*esibed es t&*s. bitity of fuetua*io*rs q*,sseheima@-$1t}' ,distrihs*fu iq{sfu arotrg "w**c'fu{€' ,T " "r El" , ? - , f & t n o " nw*x t =+€ .l** t* , * { f i l i . i fu*"*L #-v* {-} q*-ker*' sx} = rF $,e& Lry {Tryf J"f ;*r**j { l t y r r 5 n i pfff qr\ : . SL:{ id , " r.-sr.,' :' 4 I i''L- './, f :.s 6{"o1"{u**.*-dgr*' ,*a '*** " ild. F , ,r I

  2. i{(*) f {r}= t . +J ,t | 0,, t\/ r l4-Y - t \ , ) I'{ ]*e 1, Z T I x ?RACY-WIDOilI I ott$l*T_se&eraatiealtry shows the I'farEenko-pasrur form of rhe average densiry }.tl^T"t.ll- of states forc: l. Th€ever+geleiger+va{uefore : I is (I) = N. Forc: I, the I :''T':j::1-l:::9'.,:.T:T11Y)=.a},:d.!uetrratesoverascaleof*id,h,ffi of fluctuafion.s on this €cale is dsscribd by fhe Tracy-y716om distribution (shown schematicailv). scaktwl tredd&b J *t f' r .'!t .--'/3 Q z c I + {}"".-&FdJ j: i& u- N ts*,* flt b"* € k31r,i ili*-*"* = F* uxJ {.n Jr6t ? {e *d#.s** ''ry-s::r 5$6s" bg*' y5, 'lA a.f-,-aw-#*&fl MtA'fuk*ffi, "-=;: i'an*d , F* -r fu- F.S;ws, *f d 3Y.r i 6't - i."' &&{tf,tmYi4:-1' €'i

  3. *F-rs*g*td {d"s}*u* a t ., f' i *, & e* f f ,;F; *y"F {*, .i1 € ' v 1 # s " i f f r : * i i i u .dr ; *'* _......'no' ,:. **--,J- : h *F , S * I &.* €w e q}€ - e 1 t f , 1 . f , h i f { v " * s } q r H j r t r 9 #- J $ t 1 X .J' q B ? i F - d q J & & e & l 4 f i s a % * i E{x}a*}.i e t Y - t E f*" {*"#,}.* " 3 { s J l l|* tfr \ \ j ^t, "S 'dil-. ? * * bi$'* *g*.eh'mu **- _&X"9n€ * *eLng* qnt[ ho*lo7 r^n**:&-** {O;ryf" *&#* aS }d #j-'*-.g*{"} 1 t |" 4rP{s } s fl .}= *y* { rf3 d-x I *1 'fr-"*' & #cnr;fu h#'* \ i a.,,'b*fi fu , ! , / f : 1 ;-- "; l"' r+'' +"'-u*'f3 f- {* }** ,f * # f,"'-u''I t 7 { 4 r E = - J: --* *.* f*'i :c * e ! F x s l - i . l , " l l r - l \ * . i

  4. --- cD c^ . . . Y a t l -) 6 (-, n t w . d n \ : v € a \l/ - h n ir ai - 'r- d 1 il t l a rD U (1. -P c\ 'J -) I a c') . - € r - o i_i f i ) <r I ri i \ g i-r '-l hfr . . - w a .l ar: O O O il* BF* +{ F$ Lft \ \ f*; * F s r A \s 4 * H -€ ,g B* tr if !t t . * . > g e i r * l i J "J- {.J E*- I

  5. ry 5 aafu Lr:"p& &,8*-cea4=#e" i rt"*.&s; inte-gw wdthodt elwentz.+ X , { 9 , 3 , € , 4 } L , 6 , + r 1 3 "t =E -f X r i+ ,ttL/C3 -' ara or&xA *t^t+"SL .t*t*gt*c#+ i at"eryA&"c.€- ,,1tg,lt"Lh\ @uctt a, 4 6,?I 6 , 7 3 ,7-J 4&,€, , { , l4,L,tl ,+ g{-*- l**1Uk .{-=4 Af } 3 , 3 , 1 , f Y ' t Z r 6, S j , , ' 1 lt,r, f,, 6rsI l * 5 L t 5 U'k\ (^u{* Eee4 Gws;& #ff 11 ! F*-"^e***t "y*\ (tr a*L {n Ww&",ila* o **4 'Lfe;*Lh 4' rv'r"atrr'*' 45 hN t,n 'o l*?'(urr-' i*t;6, o+ is +1,,. WL.ir, 7'ttrln'r tnc) < t'h> # a''l* ^{'rl*c T,{lf**'r ( ' g t ) e t f r L ,lq1'l ) a. 2 {Vo.i^b

  6. o\ t nb Xqr^tnLe- 4 n S f incrtqs.rnt v . - - * J F#" le**y, w *7& {L* ? I s&*b*biv'- + A -L^}/*'/r {s rJ;/*'' I | {f "* } is TraeY

  7. ,i ' .r': $r6#:ri"... "*e &*.S" 4 L u-) 'rr *#' l"a,,r detailled statistics on increasing subsequences S*R . ?an;ns 4-m. $rt?*", E-* , ?ttpn# $ffi 1 {Sfqffotr* , t r n l q g t n r n < Le #* &srik, , *i, F- r'i{,,$furu-r/d*^'

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