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MATH 151 – Introduction to Probability | 2022-2023
This is the webpage for the course of Math 151 – Introduction to Probability.Lecture times: Tuesday and Thursday 9:00 AM – 10:20 AM (Room: 380-380X).Instructor: Jacopo Borga, jborga_at_stanford.edu....
View ArticleMeanders and Meandric Systems
In 1912 Henri Poincaré asked the following simple question: “In how many different ways a simple loop in the plane, called a meander, can cross a line a specified number of times?” Despite many...
View Article[16] Power-law bounds for increasing subsequences in Brownian separable...
The Brownian separable permutons are a one-parameter family – indexed by \(p \in (0, 1)\) – of universal limits of random constrained permutations. We show that for each \(p \in (0, 1)\), there are...
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Long increasing subsequences and large homogenous subsets
The length of the longest increasing subsequence in a random permutation and the size of the largest homogeneous set (i.e. a clique or an independent set) in a random graph are two of the classical...
View ArticleLong increasing subsequences in Brownian-type permutations
What is the behavior of the longest increasing subsequence of a uniformly random permutation? Its length is of order \(2n^{1/2}\) plus Tracy–Widom fluctuations of order \(n^{1/6}\). Its scaling limit...
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Meanders, meandric permutations, and meandric systems
The images on this page are taken from this work on meanders and this work on meandric systems. Meanders and meandric permutations Left: Two large uniform meanders of size 256 and 2048. Right: The...
View Article[1] The scaling limit of Baxter permutations. YoungStatS — The blog of Young...
A (rather informal) presentation of the results related to the scaling limit of Baxter permutations can be found here.
View Article[17] A determinantal point process approach to scaling and local limits of...
We obtain scaling and local limit results for large random Young tableaux of fixed shape \(\lambda^0 \) via the asymptotic analysis of a determinantal point process due to Gorin and Rahman (2019)....
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Scaling and local limits of random Young tableaux
The images on this page are taken from this work on the scaling and local limits of random Young tableaux. The heart example Figures for the heart example. Top-left: The Young diagram \(\lambda^0\)...
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MATH 159 – Discrete Probabilistic Methods | 2023-2024
This is the webpage for the course of Math 159 – Discrete Probabilistic Methods.Lecture times: Tuesday and Thursday, 1:30 PM – 2:50 PM (Hewlett Teaching Center, Rm 101).Instructor: Jacopo Borga,...
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