Alex Gamburd

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All published works

Action	Title	Year	Authors
+	An asymptotic for Markoff-Hurwitz tuples	2016	Alex Gamburd Michael Magee Ryan Ronan
+	An asymptotic formula for integer points on Markoff-Hurwitz varieties	2016	Alex Gamburd Michael Magee Ryan Ronan
+	An asymptotic formula for integer points on Markoff-Hurwitz varieties	2016	Alex Gamburd Michael Magee Ryan Ronan
+	Markoff Triples and Strong Approximation	2015	Jean Bourgain Alex Gamburd Peter Sarnak
+	Markoff Triples and Strong Approximation	2015	Jean Bourgain Alex Gamburd Peter Sarnak
+ PDF	A spectral gap theorem in SU$(d)$	2012	Jean Bourgain Alex Gamburd
+	A Spectral Gap Theorem in $SU(d)$	2011	Jean Bourgain Alex Gamburd
+ PDF	Generalization of Selberg’s $ \frac{3}{{16}} $ theorem and affine sieve	2011	Jean Bourgain Alex Gamburd Peter Sarnak
+	A Spectral Gap Theorem in $SU(d)$	2011	Jean Bourgain Alex Gamburd
+ PDF Chat	Strong Uniform Expansion in SL(2, p)	2010	Emmanuel Breuillard Alex Gamburd
+ PDF	Affine linear sieve, expanders, and sum-product	2009	Jean Bourgain Alex Gamburd Peter Sarnak
+ PDF	Expansion and random walks in $\mathrm{SL}_d(\mathbb{Z}/p^n \mathbb{Z})$: II	2009	Jean Bourgain Alex Gamburd
+	None	2009	Alex Gamburd Shlomo Hoory Mehrdad Shahshahani Aner Shalev Bálint Virág
+ PDF Chat	On the girth of random Cayley graphs	2009	Alex Gamburd Shlomo Hoory Mehrdad Shahshahani Aner Shalev Bálint Virág
+	Strong uniform expansion in $\mathrm{SL}(2,p)$	2009	Emmanuel Breuillard Alex Gamburd
+	Generalization of Selberg's 3/16 Theorem and Affine Sieve	2009	Jean Bourgain Alex Gamburd Peter Sarnak
+ PDF	Expansion and random walks in SLd(ℤ/pnℤ): I	2008	Jean Bourgain Alex Gamburd
+	Random walks and expansion in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:msub><mml:mi mathvariant="normal">SL</mml:mi><mml:mi>d</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:msup><mml:mi>p</mml:mi><mml:mi>n</mml:mi></mml:msup><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>	2008	Jean Bourgain Alex Gamburd
+ PDF	Uniform expansion bounds for Cayley graphs of SL<sub>2</sub>(𝔽<sub>p</sub>)	2008	Jean Bourgain Alex Gamburd
+	Expansion and random walks in $\mathrm {SL}_d(\mathbb {Z}/p^n\mathbb {Z})$: I	2008	Jean Bourgain Alex Gamburd
+	On the spectral gap for finitely-generated subgroups of SU(2)	2007	Jean Bourgain Alex Gamburd
+	Some applications of symmetric functions theory in random matrix theory	2007	Alex Gamburd
+ PDF	Poisson–Dirichlet distribution for random Belyi surfaces	2006	Alex Gamburd
+	Sieving and expanders⁎⁎The first author was supported in part by NSF grant DMS-0322370. The second author was supported in part by NSF grant DMS-0111298 and DMS-0501245. The third author was supported in part by Oscar Veblen Fund (IAS) and the NSF.	2006	Jean Bourgain Alex Gamburd Peter Sarnak
+	New results on expanders	2006	Jean Bourgain Alex Gamburd
+	Pseudomoments of the Riemann zeta-function and pseudomagic squares	2006	Brian Conrey Alex Gamburd
+ PDF Chat	On the Averages of Characteristic Polynomials From Classical Groups	2006	Daniel Bump Alex Gamburd
+ PDF Chat	Counting formulas associated with some random matrix averages	2005	Peter J. Forrester Alex Gamburd
+	Counting formulas associated with some random matrix averages	2005	Peter J. Forrester Alex Gamburd
+ PDF	Random Matrices, Magic Squares and Matching Polynomials	2004	Persi Diaconis Alex Gamburd
+	Uniform diameter bounds for some families of Cayley graphs	2004	Alex Gamburd Mehrdad Shahshahani
+	Eigenvalue spacings for quantized cat maps	2003	Alex Gamburd John Lafferty Dan Rockmore
+	Pseudomoments of the Riemann zeta-function and pseudomagic squares	2003	Brian Conrey Alex Gamburd
+	On the spectral gap for infinite index “congruence” subgroups of SL2(Z)	2002	Alex Gamburd
+ PDF	Spectra of elements in the group ring of $\mathrm{SU}(2)$	1999	Alex Gamburd Dmitry Jakobson Peter Sarnak

Common Coauthors

Coauthor	Papers Together
Jean Bourgain	16
Peter Sarnak	7
Ryan Ronan	3
Michael Magee	3
Mehrdad Shahshahani	3
Brian Conrey	2
Bálint Virág	2
Peter J. Forrester	2
Shlomo Hoory	2
Emmanuel Breuillard	2
Aner Shalev	2
Dan Rockmore	1
Persi Diaconis	1
John Lafferty	1
Daniel Bump	1
Dmitry Jakobson	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF	Uniform expansion bounds for Cayley graphs of SL<sub>2</sub>(𝔽<sub>p</sub>)	2008	Jean Bourgain Alex Gamburd	11
+	Bounds for multiplicities of automorphic representations	1991	Peter Sarnak Xiaoxi Xue	11
+	Cayley graphs: eigenvalues, expanders and random walks	1995	Alexander Lubotzky	10
+	Symmetric random walks on groups	1959	Harry Kesten	9
+	On the spectral gap for infinite index “congruence” subgroups of SL2(Z)	2002	Alex Gamburd	9
+ PDF	Spectra of elements in the group ring of $\mathrm{SU}(2)$	1999	Alex Gamburd Dmitry Jakobson Peter Sarnak	7
+ PDF Chat	A sum-product estimate in finite fields, and applications	2004	Jean Bourgain Nets Hawk Katz Terence Tao	7
+	On the estimation of Fourier coefficients of modular forms	1965	Atle Selberg	7
+	Groups and expanders	1993	Alexander Lubotzky Benjamin Weiss	7
+	Analytic Number Theory	2004	Henryk Iwaniec Emmanuel Kowalski	6
+ PDF Chat	Autocorrelation of Random Matrix Polynomials	2003	J. Brian Conrey David W. Farmer Jonathan P. Keating Michael Rubinstein N. C. Snaith	6
+	Ramanujan graphs	1988	Alexander Lubotzky Ralph S. Phillips Peter Sarnak	6
+	Random Matrix Theory and L-Functions at s = 1/2	2000	Jon P Keating N. C. Snaith	6
+	ESTIMATES FOR THE NUMBER OF SUMS AND PRODUCTS AND FOR EXPONENTIAL SUMS IN FIELDS OF PRIME ORDER	2006	Jean Bourgain A. A. Glibichuk Sergeĭ Konyagin	5
+ PDF	Symmetric Random Walks on Groups	1959	Harry Kesten	5
+ PDF	Random Matrices, Magic Squares and Matching Polynomials	2004	Persi Diaconis Alex Gamburd	5
+	Expanding graphs and invariant means	1997	Yehuda Shalom	5
+ PDF	The limit set of a Fuchsian group	1976	S. J. Patterson	5
+ PDF	Random Matrix Theory and ζ(1/2+ it)	2000	Jonathan P. Keating N. C. Snaith	5
+ PDF	Affine linear sieve, expanders, and sum-product	2009	Jean Bourgain Alex Gamburd Peter Sarnak	5
+	On the eigenvalues of random matrices	1994	Persi Diaconis Mehrdad Shahshahani	5
+ PDF	Growth and generation in SL<sub>2</sub>(ℤ∕pℤ)	2008	H. A. Helfgott	5
+	Free subgroups in linear groups	1972	Jacques Tits	4
+	The Asymptotic Distribution of Lattice Points in Euclidean and Non-Euclidean Spaces	1982	Peter D. Lax Ralph S. Phillips	4
+	Growth and generation in SL_2(Z/pZ)	2005	H. A. Helfgott	4
+	Geometry of Discrete Groups	2006	Alan F. Beardon	4
+ PDF Chat	Characteristic Polynomials of Random Matrices	2000	E. Brézin S. Hikami	4
+	Explicit constructions of graphs without short cycles and low density codes	1982	G. A. Margulis	4
+	Notes on the Generalized Ramanujan Conjectures	2005	Peter Sarnak	4
+	On the spectral gap for finitely-generated subgroups of SU(2)	2007	Jean Bourgain Alex Gamburd	4
+ PDF Chat	Product set estimates for non-commutative groups	2008	Terence Tao	3
+	Additive Combinatorics	2006	Terence Tao Van H. Vu	3
+	Some Applications of Modular Forms	1990	Peter Sarnak	3
+	Numerical investigation of the spectrum for certain families of Cayley graphs	1993	John Lafferty Daniel N. Rockmore	3
+	Enumerative Combinatorics	1997	Richard P. Stanley Gian‐Carlo Rota	3
+ PDF	The spectral geometry of a tower of coverings	1986	Robert Brooks	3
+	Elementary Number Theory, Group Theory and Ramanujan Graphs	2001	Giuliana P. Davidoff Peter Sarnak Alain Valette	3
+ PDF Chat	High moments of the Riemann zeta-function	2001	J. Brian Conrey S. M. Gonek	3
+	Congruence Properties of Zariski-Dense Subgroups I	1984	Christopher R. Matthews L. N. Vaserstein Boris Weisfeiler	3
+ PDF Chat	Diophantine properties of elements of SO(3)	2001	V. A. Kaloshin Igor Rodnianski	3
+ PDF	Permutations, matrices, and generalized Young tableaux	1970	Donald Knuth	3
+	Products of Random Matrices with Applications to Schrödinger Operators	1985	Philippe Bougerol Jean Lacroix	3
+ PDF	Algebraic aspects of increasing subsequences	2001	Jinho Baik Eric M. Rains	3
+ PDF Chat	Secular determinants of random unitary matrices	1996	Fritz Haake Marek Kuś Hans-Jürgen Sommers Henning Schomerus Karol Życzkowski	3
+ PDF	Increasing Subsequences and the Classical Groups	1998	Eric M. Rains	3
+ PDF	Finite Quotients of the Automorphism Group of a Free Group	1977	Robert H. Gilman	3
+	Random matrix theory and the derivative of the Riemann zeta function	2000	C. P. Hughes Jonathan P. Keating Neil 'Connell	3
+	Almost all subgroups of a Lie group are free	1971	D. B. A. Epstein	3
+ PDF Chat	Finite-N fluctuation formulas for random matrices	1997	T. H. Baker Peter J. Forrester	3
+ PDF	Discrete conformal groups and measurable dynamics	1982	Dennis Sullivan	3