Jacopo

Permutations in Random Geometry

Random geometry and random permutations have been extremely active fields of research for several years. The former is characterized by the study of large planar maps and their continuum limits, i.e. the Brownian map, Liouville quantum gravity surfaces and Schramm–Loewner evolutions. The latter is characterized by the study of large uniform permutations and (more recently) …

Permutations in Random GeometryRead More »

MATH 106 – Functions of a Complex Variable | 2022-2023

This is the webpage for the course MATH 106 – Functions of a Complex Variable. IMPORTANT NEWS: / Lecture times: Tuesday+Thursday 9:00 AM – 10:20 AM (Room: 380-380C). Instructor: Jacopo Borga (jborga_at_stanford.edu) Office hours: Tuesday 11:00-12:00 AM (Room: 382-Q2). Assistant: Judson Otto Kuhrman (kuhrman_at_stanford.edu) Office hours: Monday Wednesday (Room: ). Description: Math 106 is an introductory course on complex analysis (focused on functions of …

MATH 106 – Functions of a Complex Variable | 2022-2023Read More »

MATH 136 – Stochastic Processes | 2022-2023

This is the webpage for the course MATH 136 – Stochastic Processes. IMPORTANT NEWS: / Lecture times: Tuesday+Thursday 1:30 PM – 2:50 PM (Room: 260-113). Instructor: Jacopo Borga (jborga_at_stanford.edu) Office hours: Thursday 11:00-12:00 AM (Room: 382-Q2). Assistant: Christian Serio (cdserio_at_stanford.edu) Office hours: Wednesday 1:00-3:00 PM (Room: 381-D). Assistant: Zhongren Chen (czrbear_at_stanford.edu) Office hours: Monday 4:30-6:30 PM (Room: TBA). Description: This course prepares students to a rigorous study of …

MATH 136 – Stochastic Processes | 2022-2023Read More »

[14] Permutons, meanders, and SLE-decorated Liouville quantum gravity (with Ewain Gwynne and Xin Sun)

We study a class of random permutons which can be constructed from a pair of space-filling Schramm-Loewner evolution (SLE) curves on a Liouville quantum gravity (LQG) surface. This class includes the skew Brownian permutons introduced by Borga (2021), which describe the scaling limit of various types of random pattern-avoiding permutations. Another interesting permuton in our …

[14] Permutons, meanders, and SLE-decorated Liouville quantum gravity (with Ewain Gwynne and Xin Sun)Read More »

[13] Large deviation principle for random permutations (with Sayan Das, Sumit Mukherjee, Peter Winkler)

We derive a large deviation principle for random permutations induced by probability measures of the unit square, called permutons. These permutations are called μ-random permutations. We also introduce and study a new general class of models of random permutations, called Gibbs permutation models, which combines and generalizes μ-random permutations and the celebrated Mallows model for …

[13] Large deviation principle for random permutations (with Sayan Das, Sumit Mukherjee, Peter Winkler)Read More »

[12] Baxter permuton and Liouville quantum gravity (with Nina Holden, Xin Sun, and Pu Yu)

The Baxter permuton is a random probability measure on the unit square which describes the scaling limit of uniform Baxter permutations. We find an explict formula for the expectation of the Baxter permuton, i.e. the density of its intensity measure. This answers a question of Dokos and Pak (2014). We also prove that all pattern …

[12] Baxter permuton and Liouville quantum gravity (with Nina Holden, Xin Sun, and Pu Yu)Read More »

The skew Brownian permuton: a new universal limit for random constrained permutations and its connections with Liouville quantum gravity

Consider a large random permutation satisfying some constraints or biased according to some statistics. What does it look like? In this seminar we make sense of this question introducing the notion of permuton. Permuton convergence has been established for several models of random permutations in various works: we give an overview of some of these …

The skew Brownian permuton: a new universal limit for random constrained permutations and its connections with Liouville quantum gravityRead More »

The skew Brownian permuton

Consider a large random permutation satisfying some constraints or biased according to some statistics. What does it look like? In this seminar we make sense of this question introducing the notion of permutons. Permuton convergence has been established for several models of random permutations in various works: we give an overview of some of these results, …

The skew Brownian permutonRead More »