Doron Puder

activity

20082026

most citedExpansion of Random Graphs: New Proofs, New Results

81 citations · 383 across the 34 of their papers we have counts for

collaborators

34 papers

math.GR2026

Aldous-type Spectral Gaps in Generalized Symmetric Groups

Niv Levhari, Doron Puder

We prove an analog of Aldous' spectral gap conjecture in the generalized symmetric groups $G ≀ S_{n}$ where $G$ is an arbitrary finite group. Moreover, we show that Caputo's extensi…

math.PR2026

Aldous-type Spectral Gaps in Unitary Groups

Gil Alon, Doron Puder

Aldous' spectral gap conjecture, proven by Caputo, Liggett and Richthammer, states the following: for any set of transpositions in the symmetric group $Sym (n)$ , the spectr…

math.GR2025

Stable Invariants of Words from Random Matrices II: Formulas and Extensions

Doron Puder, Yotam Shomroni

Let $w$ be a word in a free group. As was revealed by Magee and Puder in [arXiv:1802.04862], the stable commutator length (scl) of $w$ , a well-known topological invariant, can also…

math.GT2025

Strong convergence of uniformly random permutation representations of surface groups

Michael Magee, Doron Puder, Ramon van Handel

Let $Γ$ be the fundamental group of a closed orientable surface of genus at least two. Consider the composition of a uniformly random element of $Hom (Γ, S_{n})$ with the $(n-…

math.GR2025

Primitivity Testing in Free Group Algebras via Duality

Matan Seidel, Danielle Ernst-West, Doron Puder

Let $K$ be a field and $F$ a free group. By a classical result of Cohn and Lewin, the free group algebra $K [F]$ is a free ideal ring (FIR): a ring over which the submodu…

math.CO2024

The ring of stable characters over $GL_{∙} (q)$

Danielle Ernst-West, Doron Puder, Yotam Shomroni

For a fixed prime power $q$ , let $GL_{∙} (q)$ denote the family of groups $GL_{N} (q)$ for $N \in Z_{\geq 0}$ . In this paper we study the $C$ -algebr…

math.PR2024

An extension of the cogrowth formula to arbitrary subsets of the tree

Doron Puder

What is the probability that a random walk in the free group ends in a proper power? Or in a primitive element? We present a formula that computes the exponential decay rate of the…

math.GR2023

Stable Invariants of Words from Random Matrices

Doron Puder, Yotam Shomroni, Danielle Ernst-West +1

Let $w$ be a word in a free group. A few years ago, Magee and the first named author discovered that the stable commutator length (scl) of $w$ , a well-known topological invariant,…

math.GR2023

On the Aldous-Caputo Spectral Gap Conjecture for Hypergraphs

Gil Alon, Gady Kozma, Doron Puder

In their celebrated paper (arXiv:0906.1238), Caputo, Liggett and Richthammer proved Aldous' conjecture and showed that for an arbitrary finite graph, the spectral gap of the interc…

math.GR2022

Local Statistics of Random Permutations from Free Products

Doron Puder, Tomer Zimhoni

Let $α$ and $β$ be uniformly random permutations of orders $2$ and $3$ , respectively, in $S_{N}$ , and consider, say, the permutation $α β α β^{- 1}$ . How many fixed points does this ra…

math.GR2021★ 2 cited

Word Measures on $G L_{N} (q)$ and Free Group Algebras

Danielle Ernst-West, Doron Puder, Matan Seidel

Fix a finite field $K$ of order $q$ and a word $w$ in a free group $F$ on $r$ generators. A $w$ -random element in $G L_{N} (K)$ is obtained by sampling $r$ independent uniformly random…

math.GR2021★ 3 cited

Core Surfaces

Michael Magee, Doron Puder

Let $Γ_{g}$ be the fundamental group of a closed connected orientable surface of genus $g \geq 2$ . We introduce a combinatorial structure of "core surfaces", that represent subgroups o…

math.GR2020★ 17 cited

Word Measures on Symmetric Groups

Liam Hanany, Doron Puder

Fix a word $w$ in a free group $F$ on $r$ generators. A $w$ -random permutation in the symmetric group $S_{N}$ is obtained by sampling $r$ independent uniformly random permutations $σ…

math.CO2020★ 6 cited

A Note on the Trace Method for Random Regular Graphs

Joel Friedman, Doron Puder

The main goal of this note is to illustrate the advantage of analyzing the non-backtracking spectrum of a regular graph rather than the ordinary spectrum. We show that by switching…

math.SP2020★ 24 cited

A random cover of a compact hyperbolic surface has relative spectral gap $\frac{3}{16} - ε$

Michael Magee, Frédéric Naud, Doron Puder

Let $X$ be a compact connected hyperbolic surface, that is, a closed connected orientable smooth surface with a Riemannian metric of constant curvature -1. For each $n\in\mathbf{N}…

math.GR2020★ 14 cited

The Asymptotic Statistics of Random Covering Surfaces

Michael Magee, Doron Puder

Let $Γ_{g}$ be the fundamental group of a closed connected orientable surface of genus $g \geq 2$ . We develop a new method for integrating over the representation space $\mathbb{X}_{…

math.GR2019★ 10 cited

Some Orbits of Free Words that are Determined by Measures on Finite Groups

Liam Hanany, Chen Meiri, Doron Puder

Every word in a free group $F$ induces a probability measure on every finite group in a natural manner. It is an open problem whether two words that induce the same measure on ever…

math.OA2019★ 2 cited

Automorphism-invariant positive definite functions on free groups

Benoît Collins, Michael Magee, Doron Puder

In this article we raise some new questions about positive definite functions on free groups, and explain how these are related to more well-known questions. The article is intende…

math.GT2019★ 6 cited

Matrix Group Integrals, Surfaces, and Mapping Class Groups II: $O (n)$ and $Sp (n)$

Michael Magee, Doron Puder

Let $w$ be a word in the free group on $r$ generators. The expected value of the trace of the word in $r$ independent Haar elements of $O (n)$ gives a function ${\cal T}r_{…

math.GR2019★ 5 cited

Surface Words are Determined by Word Measures on Groups

Michael Magee, Doron Puder

Every word $w$ in a free group naturally induces a probability measure on every compact group $G$ . For example, if $w = [x, y]$ is the commutator word, a random element sam…

math.GR2018★ 9 cited

Aldous' Spectral Gap Conjecture for Normal Sets

Ori Parzanchevski, Doron Puder

Let $S_{n}$ denote the symmetric group on $n$ elements, and $Σ \subseteq S_{n}$ a symmetric subset of permutations. Aldous' spectral gap conjecture, proved by Caputo, Liggett and Rich…

math.GT2018★ 21 cited

Matrix Group Integrals, Surfaces, and Mapping Class Groups I: $U (n)$

Michael Magee, Doron Puder

Since the 1970's, physicists and mathematicians who study random matrices in the GUE or GOE models are aware of intriguing connections between integrals of such random matrices and…

math.CO2017★ 4 cited

Asymptotics for a Class of Meandric Systems, via the Hasse Diagram of NC(n)

I. P. Goulden, Alexandru Nica, Doron Puder

We consider closed meandric systems, and their equivalent description in terms of the Hasse diagrams of the lattices of non-crossing partitions $N C (n)$ . In this equivalent descript…

math.NT2017★ 6 cited

The Markoff Group of Transformations in Prime and Composite Moduli

Chen Meiri, Doron Puder, Dan Carmon

The Markoff group of transformations is a group $Γ$ of affine integral morphisms, which is known to act transitively on the set of all positive integer solutions to the equation $x…

Aldous-type Spectral Gaps in Generalized Symmetric Groups

Aldous-type Spectral Gaps in Unitary Groups

Stable Invariants of Words from Random Matrices II: Formulas and Extensions

Strong convergence of uniformly random permutation representations of surface groups

Primitivity Testing in Free Group Algebras via Duality

The ring of stable characters over GL∙​(q)

An extension of the cogrowth formula to arbitrary subsets of the tree

Stable Invariants of Words from Random Matrices

On the Aldous-Caputo Spectral Gap Conjecture for Hypergraphs

Local Statistics of Random Permutations from Free Products

Word Measures on GLN​(q) and Free Group Algebras

Core Surfaces

Word Measures on Symmetric Groups

A Note on the Trace Method for Random Regular Graphs

A random cover of a compact hyperbolic surface has relative spectral gap 163​−ε

The Asymptotic Statistics of Random Covering Surfaces

Some Orbits of Free Words that are Determined by Measures on Finite Groups

Automorphism-invariant positive definite functions on free groups

Matrix Group Integrals, Surfaces, and Mapping Class Groups II: O(n) and Sp(n)

Surface Words are Determined by Word Measures on Groups

Aldous' Spectral Gap Conjecture for Normal Sets

Matrix Group Integrals, Surfaces, and Mapping Class Groups I: U(n)

Asymptotics for a Class of Meandric Systems, via the Hasse Diagram of NC(n)

The Markoff Group of Transformations in Prime and Composite Moduli

The ring of stable characters over $GL_{∙} (q)$

Word Measures on $G L_{N} (q)$ and Free Group Algebras

A random cover of a compact hyperbolic surface has relative spectral gap $\frac{3}{16} - ε$

Matrix Group Integrals, Surfaces, and Mapping Class Groups II: $O (n)$ and $Sp (n)$

Matrix Group Integrals, Surfaces, and Mapping Class Groups I: $U (n)$