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BEGIN:VEVENT
UID:b3213784fe3192d89ac1606c32a348f5
CATEGORIES:Symmetric Functions & Probability Theory Seminar
CREATED:20250226T154503
SUMMARY:Random Fibonacci Words
LOCATION:Hill 705
DESCRIPTION:Date: 03/12/2025Speaker: Leonid Petrov (https://lpetrov.cc/) (Virginia)\nTi
 tle: Random Fibonacci Words\nAbstract: Fibonacci words are words of 1's and
  2's, graded by the total sum of the digits. They form a differential poset
  YF which is an estranged cousin of the Young lattice powering irreducible 
 representations of the symmetric group. We introduce families of "coherent"
  measures on YF depending on many parameters, which come from the theory of
  clone Schur functions (Okada 1994). We characterize parameter sequences en
 suring positivity of the measures, and we describe the large-scale behavior
  of some ensembles of random Fibonacci words. The subject has connections t
 o total positivity of tridiagonal matrices, Stieltjes moment sequences, ort
 hogonal polynomials from the (q-)Askey scheme, and residual allocation (sti
 ck-breaking) models. \n
X-ALT-DESC;FMTTYPE=text/html:<h3 dir="ltr" style="line-height: 1.25; margin-top: 0pt; margin-bottom: 0pt
 ;"><span style="font-size: 11pt; font-family: Lato; color: #212121; backgro
 und-color: transparent; font-weight: bold; font-style: normal; font-variant
 : normal; text-decoration: none; vertical-align: baseline; white-space: pre
 -wrap;">Date</span><span style="font-size: 11pt; font-family: Lato; color: 
 #212121; background-color: transparent; font-weight: 400; font-style: norma
 l; font-variant: normal; text-decoration: none; vertical-align: baseline; w
 hite-space: pre-wrap;">: 03/12/2025</span></h3><p dir="ltr" style="line-hei
 ght: 1.6667; margin-top: 9pt; margin-bottom: 0pt;"><span style="font-size: 
 11pt; font-family: Lato; color: #212121; background-color: transparent; fon
 t-weight: bold; font-style: normal; font-variant: normal; text-decoration: 
 none; vertical-align: baseline; white-space: pre-wrap;">Speaker</span><span
  style="font-size: 11pt; font-family: Lato; color: #212121; background-colo
 r: transparent; font-weight: 400; font-style: normal; font-variant: normal;
  text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">:
  </span><a href="https://lpetrov.cc/" style="text-decoration: none;"><span 
 style="font-size: 11pt; font-family: Lato; color: #006580; background-color
 : transparent; font-weight: 400; font-style: normal; font-variant: normal; 
 text-decoration: underline; vertical-align: baseline; white-space: pre-wrap
 ;">Leonid Petrov</span></a><span style="font-size: 11pt; font-family: Lato;
  color: #212121; background-color: transparent; font-weight: 400; font-styl
 e: normal; font-variant: normal; text-decoration: none; vertical-align: bas
 eline; white-space: pre-wrap;"> (Virginia)</span></p><p dir="ltr" style="li
 ne-height: 1.6667; margin-top: 9pt; margin-bottom: 0pt;"><span style="font-
 size: 11pt; font-family: Lato; color: #212121; background-color: transparen
 t; font-weight: bold; font-style: normal; font-variant: normal; text-decora
 tion: none; vertical-align: baseline; white-space: pre-wrap;">Title</span><
 span style="font-size: 11pt; font-family: Lato; color: #212121; background-
 color: transparent; font-weight: 400; font-style: normal; font-variant: nor
 mal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap
 ;">: Random Fibonacci Words</span></p><p><span style="font-size: 11pt; font
 -family: Lato; color: #212121; background-color: transparent; font-weight: 
 bold; font-style: normal; font-variant: normal; text-decoration: none; vert
 ical-align: baseline; white-space: pre-wrap;">Abstract</span><span style="f
 ont-size: 11pt; font-family: Lato; color: #212121; background-color: transp
 arent; font-weight: 400; font-style: normal; font-variant: normal; text-dec
 oration: none; vertical-align: baseline; white-space: pre-wrap;">: Fibonacc
 i words are words of 1's and 2's, graded by the total sum of the digits. Th
 ey form a differential poset YF which is an estranged cousin of the Young l
 attice powering irreducible representations of the symmetric group. We intr
 oduce families of "coherent" measures on YF depending on many parameters, w
 hich come from the theory of clone Schur functions (Okada 1994). We charact
 erize parameter sequences ensuring positivity of the measures, and we descr
 ibe the large-scale behavior of some ensembles of random Fibonacci words. T
 he subject has connections to total positivity of tridiagonal matrices, Sti
 eltjes moment sequences, orthogonal polynomials from the (q-)Askey scheme, 
 and residual allocation (stick-breaking) models. </span></p>
CONTACT:Leonid Petrov
DTSTAMP:20260827T094718
DTSTART;TZID=America/New_York:20250312T104500
DTEND;TZID=America/New_York:20250312T234500
SEQUENCE:0
TRANSP:OPAQUE
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