81 citations · 383 across the 34 of their papers we have counts for
19 papers · 1 filter
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 where is an arbitrary finite group. Moreover, we show that Caputo's extensi…
Stable Invariants of Words from Random Matrices II: Formulas and Extensions
Doron Puder, Yotam Shomroni
Let be a word in a free group. As was revealed by Magee and Puder in [arXiv:1802.04862], the stable commutator length (scl) of , a well-known topological invariant, can also…
Primitivity Testing in Free Group Algebras via Duality
Matan Seidel, Danielle Ernst-West, Doron Puder
Let be a field and a free group. By a classical result of Cohn and Lewin, the free group algebra is a free ideal ring (FIR): a ring over which the submodu…
Stable Invariants of Words from Random Matrices
Doron Puder, Yotam Shomroni, Danielle Ernst-West +1
Let 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 , a well-known topological invariant,…
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…
Local Statistics of Random Permutations from Free Products
Doron Puder, Tomer Zimhoni
Let and be uniformly random permutations of orders and , respectively, in , and consider, say, the permutation . How many fixed points does this ra…
Word Measures on and Free Group Algebras
Danielle Ernst-West, Doron Puder, Matan Seidel
Fix a finite field of order and a word in a free group on generators. A -random element in is obtained by sampling independent uniformly random…
Core Surfaces
Michael Magee, Doron Puder
Let be the fundamental group of a closed connected orientable surface of genus . We introduce a combinatorial structure of "core surfaces", that represent subgroups o…
Word Measures on Symmetric Groups
Liam Hanany, Doron Puder
Fix a word in a free group on generators. A -random permutation in the symmetric group is obtained by sampling independent uniformly random permutations $σ…
The Asymptotic Statistics of Random Covering Surfaces
Michael Magee, Doron Puder
Let be the fundamental group of a closed connected orientable surface of genus . We develop a new method for integrating over the representation space $\mathbb{X}_{…
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 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…
Surface Words are Determined by Word Measures on Groups
Michael Magee, Doron Puder
Every word in a free group naturally induces a probability measure on every compact group . For example, if is the commutator word, a random element sam…
Aldous' Spectral Gap Conjecture for Normal Sets
Ori Parzanchevski, Doron Puder
Let denote the symmetric group on elements, and a symmetric subset of permutations. Aldous' spectral gap conjecture, proved by Caputo, Liggett and Rich…
Word Measures on Unitary Groups
Michael Magee, Doron Puder
We combine concepts from random matrix theory and free probability together with ideas from the theory of commutator length in groups and maps from surfaces, and establish new conn…
Growth of Primitive Elements in Free Groups
Doron Puder, Conan Wu
In the free group , an element is said to be primitive if it belongs to a free generating set. In this paper, we describe what a generic primitive element looks like. We prove…
Stallings Graphs, Algebraic Extensions and Primitive Elements in F2
Ori Parzanchevski, Doron Puder
This paper studies the free group of rank two from the point of view of Stallings core graphs. The first half of the paper examines primitive elements in this group, giving new and…
Measure Preserving Words are Primitive
Doron Puder, Ori Parzanchevski
We establish new characterizations of primitive elements and free factors in free groups, which are based on the distributions they induce on finite groups. For every finite group…
Primitive Words, Free Factors and Measure Preservation
Doron Puder
Let F_k be the free group on k generators. A word w \in F_k is called primitive if it belongs to some basis of F_k. We investigate two criteria for primitivity, and consider more g…
On Primitive Words I: A New Algorithm
Doron Puder
Let be the free group on generators, and let $H\le J\le \F_k$ be subgroups of finite rank. We present a new elementary algorithm to determine whether is a free factor…