30 citations · 128 across the 25 of their papers we have counts for
28 papers
Directed distances in spanning-tree-decorated planar maps: exact exponent, scaling limit and universality
Jacopo Borga, Ewain Gwynne, Yuanzheng Wang
We define a natural orientation on a spanning-tree-decorated planar map whereby, roughly speaking, each directed edge in the map is oriented to match the direction of the contour e…
Directed distances in bipolar-oriented triangulations: exact exponents and scaling limits
Jacopo Borga, Ewain Gwynne
We study longest and shortest directed paths in the following natural model of directed random planar maps: the uniform infinite bipolar-oriented triangulation (UIBOT), which is th…
Permuton and local limits for the Luce model
Jacopo Borga, Sourav Chatterjee, Persi Diaconis
We investigate the asymptotic properties of permutations drawn from the Luce model, a natural probabilistic framework in which permutations are generated sequentially by sampling w…
Surface sums in two-dimensional large- lattice Yang--Mills: Cancellations and explicit computations for general loops
Jacopo Borga, Sky Cao, Jasper Shogren-Knaak
In the context of two-dimensional large- lattice Yang--Mills theory, we perform a refined study of the surface sums defined in the companion work [BCSK24]. In this setting, the…
The longest increasing subsequence of Brownian separable permutons
Arka Adhikari, Jacopo Borga, Thomas Budzinski +2
We establish a scaling limit result for the length of the longest increasing subsequence of a permutation of size sampled from the Brownian sepa…
High-dimensional permutons: theory and applications
Jacopo Borga, Andrew Lin
Permutons, which are probability measures on the unit square with uniform marginals, are the natural scaling limits for sequences of (random) permutations. We introduce…
Surface sums for lattice Yang-Mills in the large- limit
Jacopo Borga, Sky Cao, Jasper Shogren-Knaak
We give a sum over weighted planar surfaces formula for Wilson loop expectations in the large- limit of strongly coupled lattice Yang-Mills theory, in any dimension. The weights…
Reconstructing SLE-decorated Liouville quantum gravity surfaces from random permutons
Jacopo Borga, Ewain Gwynne
Permutons constructed from a Liouville quantum gravity surface and a pair of space-filling Schramm-Loewner evolutions (SLEs) have been shown -- or are conjectured -- to describe th…
A determinantal point process approach to scaling and local limits of random Young tableaux
Jacopo Borga, Cédric Boutillier, Valentin Féray +1
We obtain scaling and local limit results for large random Young tableaux of fixed shape via the asymptotic analysis of a determinantal point process due to Gorin and Rahman…
Power-law bounds for increasing subsequences in Brownian separable permutons and homogeneous sets in Brownian cographons
Jacopo Borga, William Da Silva, Ewain Gwynne
The Brownian separable permutons are a one-parameter family -- indexed by -- of universal limits of random constrained permutations. We show that for each ,…
On the geometry of uniform meandric systems
Jacopo Borga, Ewain Gwynne, Minjae Park
A meandric system of size is the set of loops formed from two arc diagrams (non-crossing perfect matchings) on , one drawn above the real line and the other bel…
Permutons, meanders, and SLE-decorated Liouville quantum gravity
Jacopo Borga, Ewain Gwynne, 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…
Large deviation principle for random permutations
Jacopo Borga, Sayan Das, Sumit Mukherjee +1
We derive a large deviation principle for random permutations induced by probability measures of the unit square, called permutons. These permutations are called -random permuta…
Baxter permuton and Liouville quantum gravity
Jacopo Borga, Nina Holden, Xin Sun +1
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 expectat…
The permuton limit of strong-Baxter and semi-Baxter permutations is the skew Brownian permuton
Jacopo Borga
We recently introduced a new universal family of permutons, depending on two parameters, called skew Brownian permuton. For some specific choices of the parameters, the skew Browni…
The skew Brownian permuton: a new universality class for random constrained permutations
Jacopo Borga
We construct a new family of random permutons, called skew Brownian permuton, which describes the limits of several models of random constrained permutations. This family is parame…
Random Permutations -- A geometric point of view
Jacopo Borga
We look at geometric limits of large random non-uniform permutations. We mainly consider two theories for limits of permutations: permuton limits, introduced by Hoppen, Kohayakawa,…
Quenched law of large numbers and quenched central limit theorem for multi-player leagues with ergodic strengths
Jacopo Borga, Benedetta Cavalli
We propose and study a new model for competitions, specifically sports multi-player leagues where the initial strengths of the teams are independent i.i.d. random variables that ev…
The feasible regions for consecutive patterns of pattern-avoiding permutations
Jacopo Borga, Raul Penaguiao
We study the feasible region for consecutive patterns of pattern-avoiding permutations. More precisely, given a family of permutations avoiding a fixed set of patterns…
Scaling and local limits of Baxter permutations and bipolar orientations through coalescent-walk processes
Jacopo Borga, Mickaël Maazoun
Baxter permutations, plane bipolar orientations, and a specific family of walks in the non-negative quadrant, called tandem walks, are well-known to be related to each other throug…
The feasible region for consecutive patterns of permutations is a cycle polytope
Jacopo Borga, Raul Penaguiao
We study proportions of consecutive occurrences of permutations of a given size. Specifically, the feasible limits of such proportions on large permutations form a region, called f…
Scaling and local limits of Baxter permutations through coalescent-walk processes
Jacopo Borga, Mickaël Maazoun
Baxter permutations, plane bipolar orientations, and a specific family of walks in the non-negative quadrant are well-known to be related to each other through several bijections.…
Asymptotic normality of consecutive patterns in permutations encoded by generating trees with one-dimensional labels
Jacopo Borga
We consider uniform random permutations drawn from a family enumerated through generating trees. We develop a new general technique to establish a central limit theorem for the num…
Almost square permutations are typically square
Jacopo Borga, Enrica Duchi, Erik Slivken
A record in a permutation is a maximum or a minimum, from the left or from the right. The entries of a permutation can be partitioned into two types: the ones that are records are…