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| author | Yuchen Pei <me@ypei.me> | 2018-12-12 09:19:48 +0100 |
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| committer | Yuchen Pei <me@ypei.me> | 2018-12-12 09:19:48 +0100 |
| commit | d4731984b0162b362694629d543ec74239be9c73 (patch) | |
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| parent | fda9f1171d43462bc9c87a777c0d481168692c2b (diff) | |
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diff --git a/site/posts/2016-10-13-q-robinson-schensted-knuth-polymer.html b/site/posts/2016-10-13-q-robinson-schensted-knuth-polymer.html deleted file mode 100644 index e7c9a7e..0000000 --- a/site/posts/2016-10-13-q-robinson-schensted-knuth-polymer.html +++ /dev/null @@ -1,38 +0,0 @@ -<!doctype html> -<html lang="en"> - <head> - <meta charset="utf-8"> - <title>A \(q\)-Robinson-Schensted-Knuth algorithm and a \(q\)-polymer</title> - <link rel="stylesheet" href="../assets/css/default.css" /> - <script src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script> - <script src="../assets/js/analytics.js" type="text/javascript"></script> - </head> - <body> - <header> - <span class="logo"> - <a href="../blog.html">Yuchen's Blog</a> - </span> - <nav> - <a href="../index.html">About</a><a href="../postlist.html">All posts</a><a href="../blog-feed.xml">Feed</a> - </nav> - </header> - - <div class="main"> - <div class="bodyitem"> - <h2> A \(q\)-Robinson-Schensted-Knuth algorithm and a \(q\)-polymer </h2> - <p>Posted on 2016-10-13</p> - <p>(Latest update: 2017-01-12) In <a href="http://arxiv.org/abs/1504.00666">Matveev-Petrov 2016</a> 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.</p> -<p>This article is available at <a href="https://arxiv.org/abs/1610.03692">arXiv</a>. 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.</p> -<p><a href="%7B%7B%20site.url%20%7D%7D/assets/resources/qrsklatest.pdf">Here</a> is a “dev” version of the article, which I shall push to arXiv when it stablises. Below is the changelog.</p> -<ul> -<li>2017-01-12: Typos and grammar, arXiv v2.</li> -<li>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.</li> -<li>2016-11-13: Fixed some typos in the proof of Theorem 3.</li> -<li>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.</li> -<li>2016-10-20: Fixed a few typos. Updated some references. Added a reference: <a href="http://web.mit.edu/~shopkins/docs/rsk.pdf">a set of notes titled “RSK via local transformations”</a>. It is written by <a href="http://web.mit.edu/~shopkins/">Sam Hopkins</a> 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.</li> -</ul> - - </div> - </div> - </body> -</html> |