N. Crawford

activity

20052025

most citedMean-field driven first-order phase transitions in systems with long-range interactions

51 citations · 243 across the 25 of their papers we have counts for

collaborators

27 papers

math.CO2025

Rainbow Trees in Hypercubes

Nicholas Crawford, Maya Sankar, Carl Schildkraut +1

We prove that every proper edge-coloring of the $n$ -dimensional hypercube $Q_{n}$ contains a rainbow copy of every tree $T$ on at most $n$ edges. This result is best possible, as $Q_…

math.PR2021★ 1 cited

Random field induced order in two dimensions

Nicolas Crawford, Wioletta M. Ruszel

In this article we prove that a classical $X Y$ model subjected to weak i.i.d. random field pointing in a fixed direction exhibits residual magnetic order in $Z^{2}$ and alig…

math.PR2021★ 2 cited

Percolation transition for random forests in $d \geq 3$

Roland Bauerschmidt, Nicholas Crawford, Tyler Helmuth

The arboreal gas is the probability measure on (unrooted spanning) forests of a graph in which each forest is weighted by a factor $β > 0$ per edge. It arises as the $q \to 0$ limit o…

math.CO2021

3-colorability of graphs with minimum degree at least 6

Nicholas Crawford, Sogol Jahanbekam

Let $G$ be an $n$ -vertex graph and let $L : V (G) \to P ({1, 2, 3})$ be a list assignment over the vertices of $G$ , where each vertex with list of size 3 and of degree at most 5…

math.CO2020

Improved algorithm to determine 3-colorability of graphs with the minimum degree at least 7

Nicholas Crawford, Sogol Jahanbekam, Katerina Potika

Let $G$ be an $n$ -vertex graph with the maximum degree $Δ$ and the minimum degree $δ$ . We give algorithms with complexity $O (1.315 8^{n - 0.7 Δ (G)})$ and $O (1.3 2^{n - 0.73 Δ (G)})$ that…

math.PR2020

Macroscopic loops in the loop O(n) model via the XOR trick

Nicholas Crawford, Alexander Glazman, Matan Harel +1

The loop $O (n)$ model is a family of probability measures on collections of non-intersecting loops on the hexagonal lattice, parameterized by a loop-weight $n$ and an edge-weight $…