Local limits for permutations and generating trees

For large combinatorial structures, two main notions of convergence can be defined: scaling limits and local limits. In particular, for graphs both notions are well-studied and well-understood. For permutations only a notion of scaling limits, called permutons, has been investigated in the last decade. In the first part of the talk, we introduce a new notion of local convergence for permutations and we prove some characterizations in terms of proportions of consecutive pattern occurrences. In the second part of the talk, we investigate a new method to establish local limits for pattern-avoiding permutations using generating trees. The theory of generating trees has been widely used to enumerate families of combinatorial objects, in particular permutations. The goal of this talk is to introduce a new facet of generating trees encoding families of permutations, in order to establish probabilistic results instead of enumerative ones.

This talk is based on this work and this work.

Slides (PDF)

11/11/2021

Dartmouth College in Hanover, New Hampshire (USA), Combinatorics seminar.

20/09/2021

Stanford University, California (USA), Probability seminar.

13 thoughts on “Local limits for permutations and generating trees”

  1. My spouse and I stumbled over here coming from a different page and thought I might check things out.
    I like what I see so now i am following you. Look forward to
    finding out about your web page repeatedly.

  2. I think what you composed was very reasonable.
    But, think about this, what if you composed a catchier
    post title? I am not saying your information isn’t solid, but
    what if you added something that grabbed a person’s attention? I mean Local limits for permutations and generating trees – Jacopo Borga
    is a little vanilla. You could look at Yahoo’s front
    page and note how they create article headlines to grab people to open the
    links. You might add a video or a related pic or two to get
    readers excited about everything’ve written. In my opinion, it would make your website a little livelier.

  3. Great blog! Is your theme custom made or did you
    download it from somewhere? A design like yours with a few simple tweeks would really make my blog jump out.
    Please let me know where you got your theme.
    Thanks

  4. I’m not sure why but this weblog is loading incredibly slowfor me. Is anyone else having this issue or is it a problemon my end? I’ll check back later and see if the problem still exists.

  5. Wow, wonderful blog format! How long have you ever been blogging
    for? you made blogging look easy. The entire look of your
    web site is magnificent, let alone the content!

  6. fantastic post, very informative. I ponder why the other specialists of this sector don’t understand this.

    You should continue your writing. I’m confident, you’ve a great readers’ base already!

  7. Hey! Do you use Twitter? I’d like to follow you if that
    would be ok. I’m undoubtedly enjoying your blog and look forward to
    new posts.

  8. After study a few of the blog posts on your website now, and I truly like your way of blogging. I bookmarked it to my bookmark website list and will be checking back soon. Pls check out my web site as well and let me know what you think.

  9. An impressive share, I just given this onto a colleague who was doing a little analysis on this. And he in fact bought me breakfast because I found it for him.. smile. So let me reword that: Thnx for the treat! But yeah Thnkx for spending the time to discuss this, I feel strongly about it and love reading more on this topic. If possible, as you become expertise, would you mind updating your blog with more details? It is highly helpful for me. Big thumb up for this blog post!

  10. This is a right weblog for everyone who wants to discover this topic. You know much its nearly difficult to argue with you (not too I really would want…HaHa). You actually put a whole new spin with a topic thats been revealed for a long time. Excellent stuff, just great!

Leave a Comment

Your email address will not be published.