Nicholas M. Ercolani

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All published works

Action	Title	Year	Authors
+ PDF Chat	Yang-Mills-Higgs Equations on Spherical Orbifolds	2024	Nicholas M. Ercolani
+	Map enumeration from a dynamical perspective	2024	Nicholas M. Ercolani J. Lega Brandon Tippings
+	Ginzburg-Landau equations on non-compact Riemann surfaces	2023	Nicholas M. Ercolani Israel Michael Sigal Jingxuan Zhang
+ PDF Chat	The Poisson geometry of Plancherel formulas for triangular groups	2023	Nicholas M. Ercolani
+	Non-recursive counts of graphs on surfaces	2023	Nicholas M. Ercolani J. Lega Brandon Tippings
+ PDF Chat	Multiple scale asymptotics of map enumeration	2023	Nicholas M. Ercolani J. Lega Brandon Tippings
+ PDF Chat	Lusztig Factorization Dynamics of the Full Kostant–Toda Lattices	2023	Nicholas M. Ercolani Jonathan Ramalheira-Tsu
+	The Poisson Geometry of Plancherel Formulas for Triangular Groups	2023	Nicholas M. Ercolani
+	Map enumeration from a dynamical perspective	2023	Nicholas M. Ercolani J. Lega Brandon Tippings
+	Total positivity and spectral theory for Toeplitz Hessenberg matrix ensembles	2023	Nicholas M. Ercolani John Peca-Medlin Jonathan Ramalheira-Tsu
+ PDF Chat	A Path-Counting Analysis of Phase Shifts in Box-Ball Systems	2022	Nicholas M. Ercolani Jonathan Ramalheira-Tsu
+ PDF Chat	Dynamics of Nonpolar Solutions to the Discrete Painlevé I Equation	2022	Nicholas M. Ercolani J. Lega Brandon Tippings
+ PDF Chat	Relating random matrix map enumeration to a universal symbol calculus for recurrence operators in terms of Bessel–Appell polynomials	2022	Nicholas M. Ercolani Patrick Waters
+	Lusztig Factorization Dynamics of the Full Kostant-Toda Lattices	2022	Nicholas M. Ercolani Jonathan Ramalheira-Tsu
+	Multiple Scale Asymptotics of Map Enumeration	2022	Nicholas M. Ercolani J. Lega Brandon Tippings
+	Non-recursive Counts of Graphs on Surfaces	2022	Nicholas M. Ercolani J. Lega Brandon Tippings
+ PDF Chat	Dynamics of Non-polar Solutions to the Discrete Painlev\'e I Equation	2021	Nicholas M. Ercolani J. Lega Brandon Tippings
+ PDF Chat	The ghost-box-ball system: A unified perspective on soliton cellular automata, the RSK algorithm and phase shifts	2021	Nicholas M. Ercolani Jonathan Ramalheira-Tsu
+ PDF Chat	Integrable Mappings from a Unified Perspective	2020	Tova J. Brown Nicholas M. Ercolani
+	A PDE approach to the combinatorics of the full map enumeration problem: Exact solutions and their universal character	2019	Nicholas M. Ercolani Patrick Waters
+	Ginzburg–Landau equations on Riemann surfaces of higher genus	2019	D. Chouchkov Nicholas M. Ercolani Steven Rayan Israel Michael Sigal
+	Relating random matrix map enumeration to a universal symbol calculus for recurrence operators in terms of Bessel-Appell polynomials	2019	Nicholas M. Ercolani Patrick Waters
+	Integrable Mappings from a Unified Perspective	2019	Tova Brown Nicholas M. Ercolani
+ PDF Chat	Singularity Analysis for Heavy-Tailed Random Variables	2018	Nicholas M. Ercolani Sabine Jansen Daniel Ueltschi
+ PDF Chat	Random partitions in statistical mechanics	2014	Nicholas M. Ercolani Sabine Jansen Daniel Ueltschi
+ PDF Chat	Cycle structure of random permutations with cycle weights	2012	Nicholas M. Ercolani Daniel Ueltschi
+	Conservation Laws of Random Matrix Theory	2012	Nicholas M. Ercolani
+ PDF Chat	The continuum limit of Toda lattices for random matrices with odd weights	2012	Nicholas M. Ercolani Virgil U. Pierce
+	Conservation Laws of Random Matrix Theory	2012	Nicholas M. Ercolani
+	The Continuum Limit of Toda Lattices for Random Matrices with Odd Weights	2011	Nicholas M. Ercolani Virgil U. Pierce
+ PDF Chat	Caustics, counting maps and semi-classical asymptotics	2011	Nicholas M. Ercolani
+	The Continuum Limit of Toda Lattices for Random Matrices with Odd Weights	2011	Nicholas M. Ercolani Virgil U. Pierce
+	Caustics, counting maps and semi-classical asymptotics	2009	Nicholas M. Ercolani
+ PDF Chat	A Variational Theory for Point Defects in Patterns	2008	Nicholas M. Ercolani Shankar C. Venkataramani
+	A quick derivation of the loop equations for random matrices	2008	Nicholas M. Ercolani K. T-R McLaughlin
+ PDF Chat	Random Matrices, Graphical Enumeration and the Continuum Limit of Toda Lattices	2007	Nicholas M. Ercolani K. T-R McLaughlin Virgil U. Pierce
+ PDF Chat	A bi-Hamiltonian structure for the integrable, discrete non-linear Schrödinger system	2006	Nicholas M. Ercolani Guadalupe Lozano
+	A Quick Derivation of the Loop Equations for Random Matrices	2006	Nicholas M. Ercolani K. T-R McLaughlin
+	Random Matrices, Graphical Enumeration and the Continuum Limit of Toda Lattices	2006	Nicholas M. Ercolani K. T-R McLaughlin Virgil U. Pierce
+	None	2003	Nicholas M. Ercolani K. T-R McLaughlin
+	None	2003	Nicholas M. Ercolani S. Jin Claire Levermore Warren MacEvoy
+	The Zero-Dispersion Limit for the Odd Flows in the Focusing Zakharov-Shabat Hierarchy	2003	Nicholas M. Ercolani S. Jin C. David Levermore Warren MacEvoy
+	Asymptotics of the partition function for random matrices via Riemann-Hilbert techniques, and applications to graphical enumeration	2002	Nicholas M. Ercolani K. T-R McLaughlin
+	Bäcklund transformations for the reduced Maxwell-Bloch equations	2001	Nicholas M. Ercolani
+	Asymptotics and integrable structures for biorthogonal polynomials associated to a random two-matrix model	2001	Nicholas M. Ercolani K. T-R McLaughlin
+	Generic singularities for the steady Boussinesq equations	1997	Russel E. Caflisch Nicholas M. Ercolani Gregory V. Steele
+ PDF Chat	The behavior of the weyl function in the zero-dispersion KdV limit	1997	Nicholas M. Ercolani C. David Levermore Taiyan Zhang
+ PDF Chat	Pole dynamics and oscillations for the complex Burgers equation in the small-dispersion limit	1996	David Senouf Russel E. Caflisch Nicholas M. Ercolani
+	Defects are weak and self-dual solutions of the Cross-Newell phase diffusion equation for natural patterns	1996	Alan C. Newell T. Passot Christopher N. Bowman Nicholas M. Ercolani R. Indik
+	Geometry of singularities for the steady Boussinesq equations	1996	Russel E. Caflisch Nicholas M. Ercolani Gregory V. Steele
+ PDF Chat	Density of heat curves in the moduli space	1995	A. I. Bobenko Nicholas M. Ercolani Horst Knörrer Eugene Trubowitz
+	Attractors and transients for a perturbed periodic KdV equation: A nonlinear spectral analysis	1993	Nicholas M. Ercolani David W. McLaughlin H. Roitner
+	Multi‐valued solutions and branch point singularities for nonlinear hyperbolic or elliptic systems	1993	Russel E. Caflisch Nicholas M. Ercolani Thomas Y. Hou Yelena Landis
+	Hyperelliptic Curves that Generate Constant Mean Curvature Tori in ℝ3	1993	Nicholas M. Ercolani Horst Knörrer Eugene Trubowitz
+	The Geometry of the Full Kostant-Toda Lattice	1993	Nicholas M. Ercolani H. Flaschka Stephanie Frank Singer
+	Painlevé Balances and Dressing Transformations	1992	Nicholas M. Ercolani H. Flaschka Luc Haine
+	On the construction of a hyper-Kähler metric on the moduli space of monopoles	1991	Nicholas M. Ercolani Aninda Sinha
+	Painlevé Property and Integrability	1991	Nicholas M. Ercolani Eric D. Siggia
+	Geometry of KDV (4): Abel sums, Jacobi variety, and theta function in the scattering case	1990	Nicholas M. Ercolani H. P. McKean
+	Geometry of the modulational instability	1990	Nicholas M. Ercolani M. Gregory Forest David W. McLaughlin
+	A Quick Proof of Fay's Secant Identities	1990	Nicholas M. Ercolani H. P. McKean
+	Painlevé property and geometry	1989	Nicholas M. Ercolani Eric D. Siggia
+	Hamiltonian structure for the modulation equations of a sine-Gordon wavetrain	1987	Nicholas M. Ercolani M. Gregory Forest David W. McLaughlin Richard Montgomery
+ PDF Chat	On the weak limit of rapidly oscillating waves	1987	Luigi Chierchia Nicholas M. Ercolani David W. McLaughlin
+	ON THEWEAK LIMIT OF RAPIDLY OSCILLATINGWAVES	1987	Luigi Chierchia Nicholas M. Ercolani David W. McLaughlin
+	Painlevé property and integrability	1986	Nicholas M. Ercolani Eric D. Siggia
+	Oscillations and instabilities in near integrable PDEs	1986	Nicholas M. Ercolani M. Gregory Forest David W. McLaughlin
+	The geometry of the Hill equation and of the Neumann system	1985	Nicholas M. Ercolani H. Flaschka
+ PDF Chat	The geometry of real sine-Gordon wavetrains	1985	Nicholas M. Ercolani M. Gregory Forest

Common Coauthors

Coauthor	Papers Together
Brandon Tippings	8
J. Lega	8
K. T-R McLaughlin	7
David W. McLaughlin	6
Virgil U. Pierce	5
Jonathan Ramalheira-Tsu	5
Russel E. Caflisch	4
M. Gregory Forest	4
Eric D. Siggia	3
Daniel Ueltschi	3
H. Flaschka	3
S. Jin	2
Eugene Trubowitz	2
Sabine Jansen	2
Warren MacEvoy	2
Luigi Chierchia	2
C. David Levermore	2
Horst Knörrer	2
Israel Michael Sigal	2
Patrick Waters	2
H. P. McKean	2
Gregory V. Steele	2
A. I. Bobenko	1
Thomas Y. Hou	1
Claire Levermore	1
Tova J. Brown	1
H. Roitner	1
Richard Montgomery	1
Luc Haine	1
T. Passot	1
R. Indik	1
Yelena Landis	1
Steven Rayan	1
John Peca-Medlin	1
Patrick Waters	1
Tova Brown	1
D. Chouchkov	1
Stephanie Frank Singer	1
Aninda Sinha	1
David Senouf	1
Christopher N. Bowman	1
Taiyan Zhang	1
Shankar C. Venkataramani	1
Guadalupe Lozano	1
Jingxuan Zhang	1
Alan C. Newell	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	Random Matrices, Graphical Enumeration and the Continuum Limit of Toda Lattices	2007	Nicholas M. Ercolani K. T-R McLaughlin Virgil U. Pierce	11
+	None	2003	Nicholas M. Ercolani K. T-R McLaughlin	11
+	Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory	1999	Percy Deift T. Kriecherbauer K. T-R McLaughlin Stephanos Venakides Xin Zhou	9
+ PDF Chat	Asymptotics of the partition function of a random matrix model	2005	Pavel Bleher Alexander Its	9
+ PDF Chat	On the enumeration of planar maps	1968	W. T. Tutte	8
+	New Results on the Equilibrium Measure for Logarithmic Potentials in the Presence of an External Field	1998	Percy Deift Thomas Kriecherbauer K. T-R McLaughlin	8
+ PDF Chat	2D gravity and random matrices	1995	Philippe Di Francesco Paul Ginsparg Jean Zinn‐Justin	8
+	Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach	2000	Percy Deift	8
+ PDF Chat	Orthogonal Polynomials	1971		8
+	Logarithmic Potentials with External Fields	1997	Edward B. Saff Вилмос Тотик	7
+ PDF Chat	Caustics, counting maps and semi-classical asymptotics	2011	Nicholas M. Ercolani	7
+ PDF Chat	The continuum limit of Toda lattices for random matrices with odd weights	2012	Nicholas M. Ercolani Virgil U. Pierce	7
+	Multiphase averaging and the inverse spectral solution of the Korteweg—de Vries equation	1980	H. Flaschka M. Gregory Forest David W. McLaughlin	6
+ PDF Chat	Matrix model calculations beyond the spherical limit	1993	J. Ambjørn Leonid Chekhov Charlotte Kristjansen Yu.M. Makeenko	6
+	A continuum limit of the Toda lattice	1998	Percy Deift K. T-R McLaughlin	6
+ PDF Chat	The Map Asymptotics Constant $t_g$	2008	Edward A. Bender Zhicheng Gao L. Bruce Richmond	5
+	On Whittaker vectors and representation theory	1978	Bertram Kostant	5
+	On Freud's equations for exponential weights	1986	Alphonse Magnus	5
+ PDF Chat	A Bijection for Rooted Maps on Orientable Surfaces	2009	Guillaume Chapuy Michel Marcus Gilles Schaeffer	5
+ PDF Chat	Planar Maps and Continued Fractions	2011	Jérémie Bouttier Emmanuel Guitter	5
+	On fluctuations of eigenvalues of random Hermitian matrices	1998	Kurt Johansson	5
+	Asymptotics and integrable structures for biorthogonal polynomials associated to a random two-matrix model	2001	Nicholas M. Ercolani K. T-R McLaughlin	5
+	The isomonodromy approach to matric models in 2D quantum gravity	1992	A. S. Fokas A. R. Its A. V. Kitaev	5
+	Asymptotic zero distribution of complex orthogonal polynomials associated with Gaussian quadrature	2010	Alfredo Deaño Daan Huybrechs Arno B. J. Kuijlaars	5
+	Principles of Algebraic Geometry	1978	Phillip Griffiths Joseph Harris	5
+ PDF Chat	Topological Expansion in the Cubic Random Matrix Model	2012	Pavel Bleher Alfredo Deaño	4
+	Dispersionless Toda and Toeplitz operators	2003	Anthony M. Bloch François Golse Tanmoy Paul Alejandro Uribe	4
+	On the density of Eigenvalues of a random matrix	1960	M. L. Mehta M. Gaudin	4
+	Formal Matrix Integrals and Combinatorics of Maps	2011	Benoît Eynard	4
+ PDF Chat	The Euler characteristic of the moduli space of curves	1986	John Harer Don Zagier	4
+	Hamiltonian group actions and integrable systems	1980	William W. Symes	4
+	The spectrum of Hill's equation	1975	H. P. McKean Pierre van Moerbeke	4
+ PDF Chat	Relating random matrix map enumeration to a universal symbol calculus for recurrence operators in terms of Bessel–Appell polynomials	2022	Nicholas M. Ercolani Patrick Waters	4
+	The small dispersion limit of the Korteweg‐de Vries equation. III	1983	Peter D. Lax C. David Levermore	4
+ PDF Chat	Two-dimensional gravity and intersection theory on moduli space	1990	Edward Witten	4
+	The Geometry of the Full Kostant-Toda Lattice	1993	Nicholas M. Ercolani H. Flaschka Stephanie Frank Singer	4
+	The small dispersion limit of the Korteweg‐de Vries equation. I	1983	Peter D. Lax C. David Levermore	4
+	The solution to a generalized Toda lattice and representation theory	1979	Bertram Kostant	4
+	An algorithm for map enumeration	2006	Virgil U. Pierce	3
+ PDF Chat	Discrete Painlevé equations and their appearance in quantum gravity	1991	A. S. Fokas A. R. Its A. V. Kitaev	3
+	Integrable Hamiltonian systems and the Painlevé property	1982	Tassos Bountis Harvey Segur Franco Vivaldi	3
+ PDF Chat	Semiclassical Asymptotics of Orthogonal Polynomials, Riemann-Hilbert Problem, and Universality in the Matrix Model	1999	Pavel Bleher Alexander Its	3
+	A connection between nonlinear evolution equations and ordinary differential equations of P-type. I	1980	Mark J. Ablowitz A. Ramani Harvey Segur	3
+	Multi‐valued solutions and branch point singularities for nonlinear hyperbolic or elliptic systems	1993	Russel E. Caflisch Nicholas M. Ercolani Thomas Y. Hou Yelena Landis	3
+	Method for Solving the Sine-Gordon Equation	1973	Mark J. Ablowitz D. J. Kaup Alan C. Newell Harvey Segur	3
+ PDF Chat	Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem	1999	David Aldous Persi Diaconis	3
+	Variétés de drapeaux et réseaux de Toda	1991	H. Flaschka Luc Haine	3
+	Handbook of Mathematical Functions	1966	Donald A. McQuarrie	3
+	On the 1/n Expansion for Some Unitary Invariant Ensembles of Random Matrices	2001	Sergio Albeverio L. А. Pastur Mariya Shcherbina	3
+	Asymptotic Methods in Enumeration	1974	Edward A. Bender	3