1,259 research outputs found
Variants of geometric RSK, geometric PNG and the multipoint distribution of the log-gamma polymer
We show that the reformulation of the geometric Robinson-Schensted-Knuth
(gRSK) correspondence via local moves, introduced in \cite{OSZ14} can be
extended to cases where the input matrix is replaced by more general polygonal,
Young-diagram-like, arrays of the form \polygon. We also show that a
rearrangement of the sequence of the local moves gives rise to a geometric
version of the polynuclear growth model (PNG). These reformulations are used to
obtain integral formulae for the Laplace transform of the joint distribution of
the point-to-point partition functions of the log-gamma polymer at different
space-time points. In the case of two points at equal time and space at
distance of order , we show formally that the joint law of the
partition functions, scaled by , converges to the two-point function
of the Airy processComment: 44 pages. Proposition 3.4 and Theorem 3.5 are now stated in a more
general form and some more minor changes are made (most of them following
suggestions by a referee). To appear at IMR
A Baxter class of a different kind, and other bijective results using tableau sequences ending with a row shape
Tableau sequences of bounded height have been central to the analysis of
k-noncrossing set partitions and matchings. We show here that familes of
sequences that end with a row shape are particularly compelling and lead to
some interesting connections. First, we prove that hesitating tableaux of
height at most two ending with a row shape are counted by Baxter numbers. This
permits us to define three new Baxter classes which, remarkably, do not
obviously possess the antipodal symmetry of other known Baxter classes. We then
conjecture that oscillating tableau of height bounded by k ending in a row are
in bijection with Young tableaux of bounded height 2k. We prove this conjecture
for k at most eight by a generating function analysis. Many of our proofs are
analytic in nature, so there are intriguing combinatorial bijections to be
found.Comment: 10 pages, extended abstrac
Traces in braided categories
With any even Hecke symmetry R (that is a Hecke type solution of the
Yang-Baxter equation) we associate a quasitensor category. We formulate a
condition on R implying that the constructed category is rigid and its
commutativity isomorphisms R_{U,V} are natural. We show that this condition
leads to rescaling of the initial Hecke symmetry. We suggest a new way of
introducing traces as properly normalized categorical morphisms End(V) --> K
and deduce the corresponding normalization from categorical dimensions.Comment: Source: Revised version, a more attention is given to the problem of
trace definition and its proper normalization in braided categories with
Hecke type braidings. Minor corrections in Introduction. LaTex file, all
macros included, no figure
- …