91 citations · 303 across the 26 of their papers we have counts for
28 papers
Geometry of spherical spin glasses
Eliran Subag
Spherical spin glasses are canonical models for smooth random functions in high dimensions. In this review, we survey several interrelated lines of research on their geometric stru…
Dynamics for spherical spin glasses: Gibbs distributed initial conditions
Amir Dembo, Eliran Subag
We derive the coupled non-linear integro-differential equations for the thermodynamic limit of the empirical correlation and response functions in the Langevin dynamics at temperat…
Disordered Gibbs measures and Gaussian conditioning
Amir Dembo, Eliran Subag
We study the law of a random field evaluated at a random sample from the Gibbs measure associated to a Gaussian field . In the high-temperatu…
On Smale's 17th problem over the reals
Andrea Montanari, Eliran Subag
We consider the problem of efficiently solving a system of non-linear equations in . Addressing Smale's 17th problem stated in 1998, we consider a setting whereb…
Solving systems of Random Equations via First and Second-Order Optimization Algorithms
Andrea Montanari, Eliran Subag
We revisit the problem of solving random equations in real variables, when the equations are independent realizations of a Gaussian process in dimensions. A special cas…
Concentration for the zero set of large random polynomial systems
Eliran Subag
For random systems of polynomials in real variables which include the models of Kostlan (1987) and Shub and Smale (1993), we prove that the number of zeros on the unit…
Optimization of random high-dimensional functions: Structure and algorithms
Antonio Auffinger, Andrea Montanari, Eliran Subag
Replica symmetry breaking postulates that near optima of spin glass Hamiltonians have an ultrametric structure. Namely, near optima can be associated to leaves of a tree, and the E…
On-Site Potential Creates Complexity in Systems with Disordered Coupling
Igor Gershenzon, Bertrand Lacroix-A-Chez-Toine, Oren Raz +2
We calculate the average number of critical points of the energy landscape of a many-body system with disordered two-body interactions and a weak on-site p…
Convergence of the free energy for spherical spin glasses
Eliran Subag
We prove that the free energy of any spherical mixed -spin model converges as the dimension tends to infinity. While the convergence is a consequence of the Parisi formula,…
TAP approach for multi-species spherical spin glasses I: general theory
Eliran Subag
We develop a generalized TAP approach for the multi-species version of the spherical mixed -spin models. In particular, we prove a generalized TAP representation for the free en…
TAP approach for multi-species spherical spin glasses II: the free energy of the pure models
Eliran Subag
In a companion paper we developed the generalized TAP approach for general multi-species spherical mixed -spin models. In this paper, we use it to compute the limit of the free…
On the second moment method and RS phase of multi-species spherical spin glasses
Eliran Subag
Excluding some special cases, computing the critical inverse-temperature of a mixed -spin spin glass model is a difficult task. The only known method to calculate its valu…
Concentration of the complexity of spherical pure -spin models at arbitrary energies
Eliran Subag, Ofer Zeitouni
We consider critical points of the spherical pure -spin spin glass model with Hamiltonian $H_{N}\left(\boldsymbolσ\right)=\frac{1}{N^{\left(p-1\right)/2}}\sum_{i_{1},...,i_{p}=1…
The free energy of spherical pure -spin models -- computation from the TAP approach
Eliran Subag
We compute the free energy at all temperatures for the spherical pure -spin models from the generalized Thouless-Anderson-Palmer representation. This is the first example of a m…
Dynamics for spherical spin glasses: disorder dependent initial conditions
Amir Dembo, Eliran Subag
We derive the thermodynamic limit of the empirical correlation and response functions in the Langevin dynamics for spherical mixed -spin disordered mean-field models, starting u…
The generalized TAP free energy II
Wei-Kuo Chen, Dmitry Panchenko, Eliran Subag
In a recent paper [14], we developed the generalized TAP approach for mixed -spin models with Ising spins at positive temperature. Here we extend these results in two directions…
The generalized TAP free energy
Wei-Kuo Chen, Dmitry Panchenko, Eliran Subag
We consider the mixed -spin mean-field spin glass model with Ising spins and investigate its free energy in the spirit of the TAP approach, named after Thouless, Anderson, and P…
Following the ground-states of full-RSB spherical spin glasses
Eliran Subag
We focus on spherical spin glasses whose Parisi distribution has support of the form . For such models we construct paths from the origin to the sphere which consistently re…
Geometry and temperature chaos in mixed spherical spin glasses at low temperature - the perturbative regime
Gérard Ben Arous, Eliran Subag, Ofer Zeitouni
We study the Gibbs measure of mixed spherical -spin glass models at low temperature, in (part of) the 1-RSB regime, including, in particular, models close to pure in an appropri…
Free energy landscapes in spherical spin glasses
Eliran Subag
We introduce and analyze free energy landscapes defined by associating to any point inside the sphere a free energy calculated on a thin spherical band around it, using many orthog…
The geometry of the Gibbs measure of pure spherical spin glasses
Eliran Subag
We analyze the statics for pure -spin spherical spin glass models with , at low enough temperature. With denoting the free energy, we compute the second order…
The extremal process of critical points of the pure -spin spherical spin glass model
Eliran Subag, Ofer Zeitouni
Recently, sharp results concerning the critical points of the Hamiltonian of the -spin spherical spin glass model have been obtained by means of moments computations. In particu…
The complexity of spherical p-spin models - a second moment approach
Eliran Subag
Recently, Auffinger, Ben Arous, and Černý initiated the study of critical points of the Hamiltonian in the spherical pure -spin spin glass model, and established connections bet…
Freezing and decorated Poisson point processes
Eliran Subag, Ofer Zeitouni
The limiting extremal processes of the branching Brownian motion (BBM), the two-speed BBM, and the branching random walk are known to be randomly shifted decorated Poisson point pr…