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Probability Theory and Related Fields, ISSN 0178-8051, 06/2016, Volume 165, Issue 1-2, pp. 401 - 445
To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.1007/s00440-015-0634-8 The... 
Primary 60K35 | Secondary 82D30 | Spin glasses | Models | Statistics | Analysis
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 10/2013, Volume 323, Issue 1, pp. 417 - 447
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 10/2017, Volume 210, Issue 1, pp. 135 - 209
We analyze the statics for pure p-spin spherical spin glass models with $$p\ge 3$$ p ≥ 3 , at low enough temperature. With $$F_{N,\beta }$$ F N , β denoting... 
60G60 | Mathematics, general | Primary 60G15 | Mathematics | 82D30 | Secondary 60B20 | MATHEMATICS | CHAOS | TEMPERATURE | FLUCTUATIONS | COMPLEXITY | MODEL | FREE-ENERGY | Spin glasses | Analysis | Mathematics - Probability
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 10/2016, Volume 55, Issue 5
Journal Article
Journal of Statistical Physics, ISSN 0022-4715, 1/2019, Volume 174, Issue 2, pp. 259 - 275
In this paper, we study some properties of optimal paths in the first passage percolation on $$\mathbb {Z}^d$$ Z d and show the following: (i) the number of... 
Theoretical, Mathematical and Computational Physics | Primary 60K37 | Random geometry | Quantum Physics | First passage percolation | 82D30 | Physics | Statistical Physics and Dynamical Systems | 82A51 | Random environment | Physical Chemistry | Geodesics | Secondary 60K35 | PHYSICS, MATHEMATICAL
Journal Article
Journal of Statistical Physics, ISSN 0022-4715, 10/2018, Volume 173, Issue 2, pp. 249 - 267
In this note we prove a correlation inequality for local variables of a Gibbs field based on the connectivity in a random cluster representation of the non... 
Spin glasses | Random cluster representation | 82B44 | Theoretical, Mathematical and Computational Physics | 60G60 | Correlation inequalities | Disagreement percolation | Quantum Physics | 82D30 | Physics | Statistical Physics and Dynamical Systems | Physical Chemistry | Gibbs fields | 60J99 | PERCOLATION | PHYSICS, MATHEMATICAL | Analysis | Mathematics - Probability
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 10/2018, Volume 57, Issue 5, pp. 1 - 19
In this paper, we investigate the structure of local minimizers for the isotropic–nematic interface based on the Landau-de Gennes energy. In the absence of the... 
35J61 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | 82D30 | 35J47
Journal Article
The Annals of Probability, ISSN 0091-1798, 11/2013, Volume 41, Issue 6, pp. 4214 - 4247
We analyze the landscape of general smooth Gaussian functions on the sphere in dimension N, when N is large. We give an explicit formula for the asymptotic... 
Local minimum | Integers | Spin glasses | Infinity | Critical points | Critical values | Eigenvalues | Mathematical functions | Random variables | Random matrices | Parisi formula | Sample | STATISTICS & PROBABILITY | critical points | random matrices | spin glasses | 15A52 | 60G60 | 82D30
Journal Article
Journal of Statistical Physics, ISSN 0022-4715, 05/2018, Volume 171, Issue 4, pp. 656 - 678
We consider a random walk in dimension in a dynamic random environment evolving as an interchange process with rate . We prove that, if we choose large enough,... 
Interchange process | Limit theorems | Dynamic random environment | Random walk | Renormalisation | DYNAMIC RANDOM-ENVIRONMENTS | LARGE NUMBERS | LAW | PHYSICS, MATHEMATICAL | Mathematics - Probability | Probability | Mathematics
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 07/2016, Volume 144, Issue 7, pp. 3135 - 3150
G. Parisi predicted an important variational formula for the thermodynamic limit of the intensive free energy for a class of mean field spin glasses. In this... 
Parisi formula | Sherrington-Kirkpatrick model | Dynamic programming | MATHEMATICS | dynamic programming | MATHEMATICS, APPLIED | FORMULA
Journal Article
Annals of Probability, ISSN 0091-1798, 03/2018, Volume 46, Issue 2, pp. 605 - 686
We consider biased random walks in positive random conductances on the d-dimensional lattice in the zero-speed regime and study their scaling limits. We obtain... 
Random walks in random environments | Trap model | Zero-speed | Scaling limit | Random conductances | SPEED | DIFFUSIONS | scaling limit | PERCOLATION | DYNAMICS | CONVERGENCE | STATISTICS & PROBABILITY | random conductances | trap model | zero-speed | QUENCHED INVARIANCE-PRINCIPLES
Journal Article
Journal Article
Journal of Statistical Physics, ISSN 0022-4715, 6/2015, Volume 159, Issue 6, pp. 1306 - 1326
We consider the quadratic optimization problem $$\begin{aligned}F_n^{W,\mathbf{h}}:= \sup _{\mathbf{x}\in S^{n-1}} \left( \frac{1}{2} \mathbf{x}^T W... 
Random matrices | 60F10 | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Quantum Physics | Large deviations | 82D30 | Statistical Physics, Dynamical Systems and Complexity | Replica method | Spin glass | Physics | PHYSICS, MATHEMATICAL | Mathematics - Probability
Journal Article
Annales Henri Poincaré, ISSN 1424-0637, 8/2019, Volume 20, Issue 8, pp. 2819 - 2872
Journal Article
Annales de l'institut Henri Poincare (B) Probability and Statistics, ISSN 0246-0203, 02/2018, Volume 54, Issue 1, pp. 363 - 384
We prove a quenched central limit theorem for balanced random walks in time-dependent ergodic random environments which is not necessarily nearest-neighbor. We... 
Random walk in random environment | Maximum principle | Quenched central limit theorem | PARABOLIC DIFFERENCE-OPERATORS | STOCHASTIC HOMOGENIZATION | BALLISTIC RANDOM-WALKS | EQUATIONS | STATISTICS & PROBABILITY | ZERO-RANGE PROCESS
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 4/2017, Volume 56, Issue 2, pp. 1 - 15
In this paper, we investigate the structure and stability of the isotropic-nematic interface in 1-D. In the absence of the anisotropic energy, the uniaxial... 
35A15 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 76A15 | Mathematics | 82D30 | 35J57 | MATHEMATICS | MATHEMATICS, APPLIED | PHASE | HARD SPHEROCYLINDERS | LIQUID-CRYSTALS | Anisotropy
Journal Article
The Annals of Applied Probability, ISSN 1050-5164, 8/2008, Volume 18, Issue 4, pp. 1619 - 1635
We consider branching random walks in d-dimensional integer lattice with time-space i.i.d. offspring distributions. When d ≥ 3 and the fluctuation of the... 
Comets | Transition probabilities | Population growth | Central limit theorem | Random walk | Randomness | Markov chains | Polymers | Martingales | Random environment | Branching random walk | Directed polymers | Phase transition | central limit theorem | random environment | DISORDER | branching random walk | STATISTICS & PROBABILITY | DIFFUSION | phase transition | directed polymers | 60J80 | 60K37 | 82D30 | 60K35 | 60F05
Journal Article
The Annals of Applied Probability, ISSN 1050-5164, 2/2015, Volume 25, Issue 1, pp. 116 - 149
Journal Article
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