diff options
Diffstat (limited to 'posts/2016-10-13-q-robinson-schensted-knuth-polymer.md')
| -rw-r--r-- | posts/2016-10-13-q-robinson-schensted-knuth-polymer.md | 23 |
1 files changed, 0 insertions, 23 deletions
diff --git a/posts/2016-10-13-q-robinson-schensted-knuth-polymer.md b/posts/2016-10-13-q-robinson-schensted-knuth-polymer.md deleted file mode 100644 index 4a5f793..0000000 --- a/posts/2016-10-13-q-robinson-schensted-knuth-polymer.md +++ /dev/null @@ -1,23 +0,0 @@ ---- -template: oldpost -title: A \(q\)-Robinson-Schensted-Knuth algorithm and a \(q\)-polymer -date: 2016-10-13 -comments: true -archive: false ---- -(Latest update: 2017-01-12) -In [Matveev-Petrov 2016](http://arxiv.org/abs/1504.00666) a \\(q\\)-deformed Robinson-Schensted-Knuth algorithm (\\(q\\)RSK) was introduced. In this article we give reformulations of this algorithm in terms of Noumi-Yamada description, growth diagrams and local moves. We show that the algorithm is symmetric, namely the output tableaux pair are swapped in a sense of distribution when the input matrix is transposed. We also formulate a \\(q\\)-polymer model based on the \\(q\\)RSK and prove the corresponding Burke property, which we use to show a strong law of large numbers for the partition function given stationary boundary conditions and \\(q\\)-geometric weights. We use the \\(q\\)-local moves to define a generalisation of the \\(q\\)RSK taking a Young diagram-shape of array as the input. We write down the joint distribution of partition functions in the space-like direction of the \\(q\\)-polymer in \\(q\\)-geometric environment, formulate a \\(q\\)-version of the multilayer polynuclear growth model (\\(q\\)PNG) and write down the joint distribution of the \\(q\\)-polymer partition functions at a fixed time. - -This article is available at [arXiv](https://arxiv.org/abs/1610.03692). -It seems to me that one difference between arXiv and Github is that on arXiv each preprint has a few versions only. -In Github many projects have a "dev" branch hosting continuous updates, whereas the master branch is where the stable releases live. - -[Here]({{ site.url }}/assets/qrsklatest.pdf) is a "dev" version of the article, which I shall push to arXiv when it stablises. Below is the changelog. - -* 2017-01-12: Typos and grammar, arXiv v2. -* 2016-12-20: Added remarks on the geometric \\(q\\)-pushTASEP. Added remarks on the converse of the Burke property. Added natural language description of the \\(q\\)RSK. Fixed typos. -* 2016-11-13: Fixed some typos in the proof of Theorem 3. -* 2016-11-07: Fixed some typos. The \\(q\\)-Burke property is now stated in a more symmetric way, so is the law of large numbers Theorem 2. -* 2016-10-20: Fixed a few typos. Updated some references. Added a reference: [a set of notes titled "RSK via local transformations"](http://web.mit.edu/~shopkins/docs/rsk.pdf). -It is written by [Sam Hopkins](http://web.mit.edu/~shopkins/) in 2014 as an expository article based on MIT combinatorics preseminar presentations of Alex Postnikov. -It contains some idea (applying local moves to a general Young-diagram shaped array in the order that matches any growth sequence of the underlying Young diagram) which I thought I was the first one to write down. |