## 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.

Finite sums and interpolation formulas over $GF[p^n,x]$Volume 15, Number 4 (1948)
The asymptotic expansion of Minakshisundaram-Pleijel in the equivariant caseVolume 51, Number 4 (1984)
A framework of Rogers–Ramanujan identities and their arithmetic propertiesVolume 165, Number 8 (2016)
On isometry groups and maximal symmetryVolume 162, Number 10 (2013)
Extremal metrics on blowupsVolume 157, Number 1 (2011)
• 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 (2014): 2.08
JCR (2014) Impact Factor: 1.578
JCR (2014) Five-year Impact Factor: 2.009
JCR (2014) Ranking: 18/310 (Mathematics)
Eigenfactor: Duke Mathematical Journal
SJR/SCImago Journal Rank (2014): 4.592

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

#### Random walks in the group of Euclidean isometries and self-similar measures

Volume 165, Number 6
##### Abstract

We study products of random isometries acting on Euclidean space. Building on previous work of the second author, we prove a local limit theorem for balls of shrinking radius with exponential speed under the assumption that a Markov operator associated to the rotation component of the isometries has spectral gap. We also prove that certain self-similar measures are absolutely continuous with smooth densities. These families of self-similar measures give higher-dimensional analogues of Bernoulli convolutions on which absolute continuity can be established for contraction ratios in an open set.