## Duke Mathematical Journal

Published by Duke University Press since its inception in 1935, the Duke Mathematical Journal is one of the world's leading mathematical journals. DMJ emphasizes the most active and influential areas of current mathematics. Advance publication of articles online is available.

The fundamental lemma for stable base changeVolume 61, Number 1 (1990)
Partial Fourier–Mukai transform for integrable systems with applications to Hitchin fibrationVolume 165, Number 15 (2016)
Serrin’s result for hyperbolic space and sphereVolume 91, Number 1 (1998)
Cohomology and representations of associative algebrasVolume 14, Number 4 (1947)
Matrix integrals, Toda symmetries, Virasoro constraints, and orthogonal polynomialsVolume 80, Number 3 (1995)
• ISSN: 0012-7094 (print), 1547-7398 (electronic)
• Publisher: Duke University Press
• Discipline(s): Mathematics
• Full text available in Euclid: 1935--
• Access: By subscription only
• Euclid URL: http://projecteuclid.org/dmj

### Featured bibliometrics

MR Citation Database MCQ (2015): 2.29
JCR (2015) Impact Factor: 2.350
JCR (2015) Five-year Impact Factor: 2.337
JCR (2015) Ranking: 9/312 (Mathematics)
Article Influence: 3.899
Eigenfactor: Duke Mathematical Journal
SJR/SCImago Journal Rank (2015): 5.675

Indexed/Abstracted in: CompuMath Citation Index, Current Contents: Physical, Chemical, and Earth Sciences, International Bibliography of Periodical Literature (IBZ), ISI Science Citation Index Expanded, Magazines for Libraries, MathSciNet, Scopus, zbMATH

### Featured article

#### Quantum Loewner evolution

What is the scaling limit of diffusion-limited aggregation (DLA) in the plane? This is an old and famously difficult question. One can generalize the question in two ways: first, one may consider the dielectric breakdown model$\eta$-DBM, a generalization of DLA in which particle locations are sampled from the $\eta$th power of harmonic measure, instead of harmonic measure itself. Second, instead of restricting attention to deterministic lattices, one may consider $\eta$-DBM on random graphs known or believed to converge in law to a Liouville quantum gravity (LQG) surface with parameter $\gamma\in[0,2]$.
In this generality, we propose a scaling limit candidate called quantum Loewner evolution, $\operatorname{QLE}(\gamma^{2},\eta)$. $\operatorname{QLE}$ is defined in terms of the radial Loewner equation like radial stochastic Loewner evolution, except that it is driven by a measure-valued diffusion $\nu_{t}$ derived from LQG rather than a multiple of a standard Brownian motion. We formalize the dynamics of $\nu_{t}$ using a stochastic partial differential equation. For each $\gamma\in(0,2]$, there are two or three special values of $\eta$ for which we establish the existence of a solution to these dynamics and explicitly describe the stationary law of $\nu_{t}$.
We propose $\operatorname{QLE}(2,1)$ as a scaling limit for DLA on a random spanning-tree-decorated planar map and $\operatorname{QLE}(8/3,0)$ as a scaling limit for the Eden model on a random triangulation. We propose using $\operatorname{QLE}(8/3,0)$ to endow pure LQG with a distance function, by interpreting the region explored by a branching variant of $\operatorname{QLE}(8/3,0)$, up to a fixed time, as a metric ball in a random metric space.