Annals of Probability, ISSN 0091-1798, 2017, Volume 45, Issue 6, pp. 4419 - 4476

Journal Article

Mathematical Physics, Analysis and Geometry, ISSN 1385-0172, 3/2016, Volume 19, Issue 1, pp. 1 - 87

.... The focus is on the annealed free energy per monomer in the limit as the length of the polymer chain tends to infinity...

82B44 | Theoretical, Mathematical and Computational Physics | 82B41 | Charged polymer | Large deviations | Physics | Geometry | Analysis | Ballistic vs. subballistic phase | Scaling | Group Theory and Generalizations | 60K37 | Applications of Mathematics | Quenched vs. annealed free energy | Phase transition | MATHEMATICS, APPLIED | RANDOM SELF-INTERACTIONS | ENERGY | DIRECTED WALKS | PHYSICS, MATHEMATICAL | EDWARDS MODEL | TAILS | CENTRAL-LIMIT-THEOREM | Polymers | Polymer industry | Mathematics - Probability | Probability | Mathematics

82B44 | Theoretical, Mathematical and Computational Physics | 82B41 | Charged polymer | Large deviations | Physics | Geometry | Analysis | Ballistic vs. subballistic phase | Scaling | Group Theory and Generalizations | 60K37 | Applications of Mathematics | Quenched vs. annealed free energy | Phase transition | MATHEMATICS, APPLIED | RANDOM SELF-INTERACTIONS | ENERGY | DIRECTED WALKS | PHYSICS, MATHEMATICAL | EDWARDS MODEL | TAILS | CENTRAL-LIMIT-THEOREM | Polymers | Polymer industry | Mathematics - Probability | Probability | Mathematics

Journal Article

Electronic Communications in Probability, ISSN 1083-589X, 07/2014, Volume 19, pp. 1 - 14

.... Our result generalizes the large deviation principle given by Kiesel and Stadtmuller [9] as well as the tail asymptotics for sums of i.i.d...

Kernels | Self-normalized weights | Stretched exponential random variables | Nonparametric regression | Subexponential random variables | Large deviations | Quenched and annealed large deviations | Weighted sums | self-normalized weights | weighted sums | nonparametric regression | quenched and annealed large deviations | subexponential random variables | kernels | STATISTICS & PROBABILITY | stretched exponential random variables | Mathematics - Probability

Kernels | Self-normalized weights | Stretched exponential random variables | Nonparametric regression | Subexponential random variables | Large deviations | Quenched and annealed large deviations | Weighted sums | self-normalized weights | weighted sums | nonparametric regression | quenched and annealed large deviations | subexponential random variables | kernels | STATISTICS & PROBABILITY | stretched exponential random variables | Mathematics - Probability

Journal Article

Probability theory and related fields, ISSN 0178-8051, 2010, Volume 148, Issue 3, pp. 403 - 456

.... In the annealed large deviation principle (LDP) for the empirical process of words, the rate function is the specific relative entropy of the observed law of words w.r.t...

Annealed vs. quenched | Specific relative entropy | Empirical process | Large deviation principle | 60G10 | 60F10 | Theoretical, Mathematical and Computational Physics | Renewal process | Rate function | Probability Theory and Stochastic Processes | Mathematics | Quantitative Finance | Statistics for Business/Economics/Mathematical Finance/Insurance | Letters and words | Operations Research/Decision Theory | Mathematical Biology in General | STATISTICS & PROBABILITY | Studies | Probability | Entropy | Mathematical analysis | Origins | Annealing | Algebra | Law | Stochastic systems | Deviation | Quenching (cooling)

Annealed vs. quenched | Specific relative entropy | Empirical process | Large deviation principle | 60G10 | 60F10 | Theoretical, Mathematical and Computational Physics | Renewal process | Rate function | Probability Theory and Stochastic Processes | Mathematics | Quantitative Finance | Statistics for Business/Economics/Mathematical Finance/Insurance | Letters and words | Operations Research/Decision Theory | Mathematical Biology in General | STATISTICS & PROBABILITY | Studies | Probability | Entropy | Mathematical analysis | Origins | Annealing | Algebra | Law | Stochastic systems | Deviation | Quenching (cooling)

Journal Article

Electronic Communications in Probability, ISSN 1083-589X, 03/2014, Volume 19, pp. 1 - 16

.... sequence of words is obtained. In the annealed LDP (large deviation principle) for the empirical process of words, the rate function is the specific relative entropy of the observed law of words w.r.t...

Renewal times | Specific relative entropy | Mixing | Empirical process | Letters and words | Rate function | Annealed vs. quenched large deviation principle | renewal times | mixing | empirical process | rate function | STATISTICS & PROBABILITY | annealed vs. quenched large deviation principle | specific relative entropy | UNIQUENESS | Probability | Mathematics

Renewal times | Specific relative entropy | Mixing | Empirical process | Letters and words | Rate function | Annealed vs. quenched large deviation principle | renewal times | mixing | empirical process | rate function | STATISTICS & PROBABILITY | annealed vs. quenched large deviation principle | specific relative entropy | UNIQUENESS | Probability | Mathematics

Journal Article

The Annals of Probability, ISSN 0091-1798, 5/2013, Volume 41, Issue 3, pp. 1767 - 1805

.... Using quenched and annealed large deviation principles for the empirical process of words drawn from a random letter sequence according to a random renewal process...

Ergodic theory | Random walk | Markov chains | Entropy | Mathematical functions | Critical temperature | Random variables | Polymers | Free energy | Quenched vs. annealed large deviation principle | Random charges | Random polymer | Relevant vs. irrelevant disorder | Quenched vs. annealed critical curve | Localization vs. delocalization | random charges | quenched vs. annealed critical curve | DEPINNING TRANSITIONS | localization vs. delocalization | STATISTICS & PROBABILITY | CRITICAL-POINTS | quenched vs. annealed large deviation principle | critical temperature | relevant vs. irrelevant disorder | MODELS | RELEVANCE | DISORDER | Mathematics - Probability | 82B27 | 60F10 | 82B44 | 60K37

Ergodic theory | Random walk | Markov chains | Entropy | Mathematical functions | Critical temperature | Random variables | Polymers | Free energy | Quenched vs. annealed large deviation principle | Random charges | Random polymer | Relevant vs. irrelevant disorder | Quenched vs. annealed critical curve | Localization vs. delocalization | random charges | quenched vs. annealed critical curve | DEPINNING TRANSITIONS | localization vs. delocalization | STATISTICS & PROBABILITY | CRITICAL-POINTS | quenched vs. annealed large deviation principle | critical temperature | relevant vs. irrelevant disorder | MODELS | RELEVANCE | DISORDER | Mathematics - Probability | 82B27 | 60F10 | 82B44 | 60K37

Journal Article

ANNALS OF PROBABILITY, ISSN 0091-1798, 11/2017, Volume 45, Issue 6B, pp. 4419 - 4476

...) ball in R-n onto an independent random vector from the unit sphere. We show that sequences of such random projections, when suitably normalized, satisfy a large deviation principle (LDP...

MODERATE DEVIATIONS | EMPIRICAL PROCESSES | random projections | THEOREM | STABILITY | variational formula | EXCHANGEABLE RANDOM-VARIABLES | STATISTICS & PROBABILITY | Large deviations | CONVEX-SETS | central limit theorem for convex sets | RANDOM ENVIRONMENT | l(p)-balls | annealed and quenched large deviations | DISTRIBUTIONS | RANDOM-WALKS | self-normalized large deviations | HIGH DIMENSION

MODERATE DEVIATIONS | EMPIRICAL PROCESSES | random projections | THEOREM | STABILITY | variational formula | EXCHANGEABLE RANDOM-VARIABLES | STATISTICS & PROBABILITY | Large deviations | CONVEX-SETS | central limit theorem for convex sets | RANDOM ENVIRONMENT | l(p)-balls | annealed and quenched large deviations | DISTRIBUTIONS | RANDOM-WALKS | self-normalized large deviations | HIGH DIMENSION

Journal Article

8.
Full Text
Crossing Speeds of Random Walks Among “Sparse” or “Spiky” Bernoulli Potentials on Integers

Journal of Statistical Physics, ISSN 0022-4715, 7/2013, Volume 152, Issue 2, pp. 213 - 236

...≤1, independently at each site of $\mathbb {Z}$ . We consider the walk under both quenched and annealed measures...

Random potential | Speed | Physical Chemistry | Annealed | Theoretical, Mathematical and Computational Physics | Random walk | Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Physics | Quenched | TRANSITION | LYAPUNOV EXPONENTS | BOUNDS | PHYSICS, MATHEMATICAL | LARGE DEVIATIONS

Random potential | Speed | Physical Chemistry | Annealed | Theoretical, Mathematical and Computational Physics | Random walk | Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Physics | Quenched | TRANSITION | LYAPUNOV EXPONENTS | BOUNDS | PHYSICS, MATHEMATICAL | LARGE DEVIATIONS

Journal Article

Electronic Journal of Probability, ISSN 1083-6489, 2017, Volume 22

.... The environment is temporally independent and spatially translation invariant. We study the rate functions of the level-3 averaged and quenched large deviation principles from the point of view of the particle...

Specific relative entropy | Dynamic random environment | Empirical process | Nonstationary process | Random walk | Large deviations | Doob h-transform | Donsker-Varadhan relative entropy | Averaged | Quenched | large deviations | nonstationary process | quenched | SURE INVARIANCE-PRINCIPLE | empirical process | dynamic random environment | STATISTICS & PROBABILITY | TIME | VARIATIONAL FORMULAS | random walk | ASYMPTOTIC EVALUATION | MARKOV PROCESS EXPECTATIONS | averaged | FREE-ENERGY | specific relative entropy

Specific relative entropy | Dynamic random environment | Empirical process | Nonstationary process | Random walk | Large deviations | Doob h-transform | Donsker-Varadhan relative entropy | Averaged | Quenched | large deviations | nonstationary process | quenched | SURE INVARIANCE-PRINCIPLE | empirical process | dynamic random environment | STATISTICS & PROBABILITY | TIME | VARIATIONAL FORMULAS | random walk | ASYMPTOTIC EVALUATION | MARKOV PROCESS EXPECTATIONS | averaged | FREE-ENERGY | specific relative entropy

Journal Article

Electronic journal of probability, ISSN 1083-6489, 2011, Volume 16, Issue 20, pp. 552 - 586

...), a quenched large deviation principle (LDP) has been established for the empirical process of words obtained by cutting an i.i.d...

Annealed vs. quenched | Large deviation principle | Collision local time | Random walks | Interacting stochastic systems | Intermediate phase | annealed vs. quenched | intermediate phase | DIRECTED POLYMERS | STATISTICS & PROBABILITY | ITERATED LOGARITHM | WEAK DISORDER | PINNING MODEL | RANDOM ENVIRONMENT | collision local time | TRANSITION | interacting stochastic systems | large deviation principle

Annealed vs. quenched | Large deviation principle | Collision local time | Random walks | Interacting stochastic systems | Intermediate phase | annealed vs. quenched | intermediate phase | DIRECTED POLYMERS | STATISTICS & PROBABILITY | ITERATED LOGARITHM | WEAK DISORDER | PINNING MODEL | RANDOM ENVIRONMENT | collision local time | TRANSITION | interacting stochastic systems | large deviation principle

Journal Article

Bernoulli, ISSN 1350-7265, 02/2017, Volume 23, Issue 1, pp. 405 - 431

.... case, we also give two variational formulas (aVar1) and (aVar2) for the annealed free energy of RWRP...

Weak disorder | Random potential | Random environment | KPZ universality | Random walk | Directed polymer | Quenched free energy | Variational formula | Very strong disorder | Strong disorder | Large deviation | LOCALIZATION | EXPONENTS | strong disorder | variational formula | DIRECTED POLYMERS | STATISTICS & PROBABILITY | random potential | QUENCHED LARGE DEVIATIONS | HOMOGENIZATION | very strong disorder | weak disorder | random walk | random environment | DIFFUSION | large deviation | directed polymer | FREE-ENERGY | quenched free energy | Mathematics - Probability

Weak disorder | Random potential | Random environment | KPZ universality | Random walk | Directed polymer | Quenched free energy | Variational formula | Very strong disorder | Strong disorder | Large deviation | LOCALIZATION | EXPONENTS | strong disorder | variational formula | DIRECTED POLYMERS | STATISTICS & PROBABILITY | random potential | QUENCHED LARGE DEVIATIONS | HOMOGENIZATION | very strong disorder | weak disorder | random walk | random environment | DIFFUSION | large deviation | directed polymer | FREE-ENERGY | quenched free energy | Mathematics - Probability

Journal Article

The Annals of Probability, ISSN 0091-1798, 3/2011, Volume 39, Issue 2, pp. 471 - 506

We consider large deviations for nearest-neighbor random walk in a uniformly elliptic i.i.d. environment on ${\Bbb Z}^{d...

Ergodic theory | Harmonic functions | Economic theory | Random walk | Spacetime | Markov chains | Mathematics | Mathematical functions | Entropy | Perceptron convergence procedure | Random environment | Large deviations | Doob h-transform | large deviations | LARGE NUMBERS | LAW | random environment | STATISTICS & PROBABILITY | MIXING RANDOM ENVIRONMENT | harmonic functions | QUENCHED LARGE DEVIATIONS | Mathematics - Probability | 60F10 | 60K37 | 82C41

Ergodic theory | Harmonic functions | Economic theory | Random walk | Spacetime | Markov chains | Mathematics | Mathematical functions | Entropy | Perceptron convergence procedure | Random environment | Large deviations | Doob h-transform | large deviations | LARGE NUMBERS | LAW | random environment | STATISTICS & PROBABILITY | MIXING RANDOM ENVIRONMENT | harmonic functions | QUENCHED LARGE DEVIATIONS | Mathematics - Probability | 60F10 | 60K37 | 82C41

Journal Article

Annales de l'institut Henri Poincare (B) Probability and Statistics, ISSN 0246-0203, 08/2010, Volume 46, Issue 3, pp. 853 - 868

In his 2003 paper, Varadhan proves the averaged large deviation principle for the mean velocity of a particle taking a nearest-neighbor random walk in a uniformly elliptic i.i.d. environment on Z(d) with d...

Disordered media | Regeneration times | Rare events | Rate function | DIMENSIONAL RANDOM-WALK | STATISTICS & PROBABILITY | REVERSIBLE MARKOV-PROCESSES | QUENCHED LARGE DEVIATIONS | 60F10 | 82C44 | 60K37

Disordered media | Regeneration times | Rare events | Rate function | DIMENSIONAL RANDOM-WALK | STATISTICS & PROBABILITY | REVERSIBLE MARKOV-PROCESSES | QUENCHED LARGE DEVIATIONS | 60F10 | 82C44 | 60K37

Journal Article

Journal of Theoretical Probability, ISSN 0894-9840, 01/2016, Volume 30, Issue 3

We consider a continuum percolation model on $\R^d$, $d\geq 1$.For $t,\lambda\in (0,\infty)$ and $d\in\{1,2,3\}$, the occupied set is given by the union of...

Probability | Mathematics

Probability | Mathematics

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 12/2002, Volume 124, Issue 4, pp. 487 - 516

... (which is also independent of ϕ), for every x in a large region , with N a positive integer and D a bounded subset of ℝ d...

Quenched and Annealed Models | Harmonic Crystal | Gaussian fields | Random Walks | Large Deviations | Entropic Repulsion | Rough Substrate | Extrema of Random Fields | entropic repulsion | large deviations | random walks | extrema of random fields | quenched and annealed models | harmonic crystal | STATISTICS & PROBABILITY | rough substrate | DIFFUSION EQUATION | FREE-FIELD

Quenched and Annealed Models | Harmonic Crystal | Gaussian fields | Random Walks | Large Deviations | Entropic Repulsion | Rough Substrate | Extrema of Random Fields | entropic repulsion | large deviations | random walks | extrema of random fields | quenched and annealed models | harmonic crystal | STATISTICS & PROBABILITY | rough substrate | DIFFUSION EQUATION | FREE-FIELD

Journal Article

Annales de l'institut Henri Poincare (B) Probability and Statistics, ISSN 0246-0203, 05/2010, Volume 46, Issue 2, pp. 414 - 441

.... We show that in dimensions d = 1, 2, the annealed and quenched...

Pinning models | Annealed and quenched critical points | Disordered system | Collision local time | Random walks | DIRECTED POLYMERS | STATISTICS & PROBABILITY | COPOLYMERS | TIME | WEAK DISORDER | RANDOM ENVIRONMENT | 82B44 | 60K35

Pinning models | Annealed and quenched critical points | Disordered system | Collision local time | Random walks | DIRECTED POLYMERS | STATISTICS & PROBABILITY | COPOLYMERS | TIME | WEAK DISORDER | RANDOM ENVIRONMENT | 82B44 | 60K35

Journal Article

Proceedings of the International Congress of Mathematicians 2010, ICM 2010, 2010, pp. 2258 - 2274

Conference Proceeding

Electronic Journal of Probability, ISSN 1083-6489, 2016, Volume 21

We consider a one dimensional random walk in a random environment (RWRE) with wa positive speed lim(n ->infinity) X-n/n = v(alpha) > 0. Gantert and Zeitouni...

Random walk in random environment | Large deviations | Quenched | large deviations | LIMITS | STATISTICS & PROBABILITY | quenched | random walk in random environment | TRANSIENT

Random walk in random environment | Large deviations | Quenched | large deviations | LIMITS | STATISTICS & PROBABILITY | quenched | random walk in random environment | TRANSIENT

Journal Article

MARKOV PROCESSES AND RELATED FIELDS, ISSN 1024-2953, 2012, Volume 18, Issue 4, pp. 595 - 612

...) similar to D/n for some constant D > 0 (n -> infinity), the decay rates to zero of the quenched and annealed Lyapunov exponents coincide and equal cn(-1/2...

SURVIVAL | quenched | STATISTICS & PROBABILITY | random potential | Green function | ANNEALED LYAPOUNOV EXPONENTS | Combes - Thomas estimate | Brownian motion | OPERATOR | WIENER SAUSAGE | Lyapunov exponent | ASYMPTOTICS | LARGE DEVIATIONS | annealed

SURVIVAL | quenched | STATISTICS & PROBABILITY | random potential | Green function | ANNEALED LYAPOUNOV EXPONENTS | Combes - Thomas estimate | Brownian motion | OPERATOR | WIENER SAUSAGE | Lyapunov exponent | ASYMPTOTICS | LARGE DEVIATIONS | annealed

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 5/2007, Volume 138, Issue 1, pp. 177 - 193

...)$$ satisfy a law of large numbers, or put another way, they exhibit annealed behavior. For $$\gamma > \eta(2)$$ and L(t) = eγ t , one has $$\sum_{x\in \Lambda_L}u(t,x)$$ when properly normalized and centered satisfies a central limit theorem...

Primary 60F05 | Mathematical and Computational Physics | Secondary 60G70 | Parabolic Anderson model | Probability Theory and Stochastic Processes | Mathematics | Quantitative Finance | Annealed asymptotics | Quenched asymptotics | Central limit theorem | Statistics for Business/Economics/Mathematical Finance/Insurance | Operations Research/Decision Theory | Law of large numbers | Mathematical Biology in General | Secondary 60E07 | Primary 60F10 | STATISTICS & PROBABILITY | central limit theorem | law of large numbers | annealed asymptotics | parabolic Anderson model | quenched asymptotics | Submarine boats

Primary 60F05 | Mathematical and Computational Physics | Secondary 60G70 | Parabolic Anderson model | Probability Theory and Stochastic Processes | Mathematics | Quantitative Finance | Annealed asymptotics | Quenched asymptotics | Central limit theorem | Statistics for Business/Economics/Mathematical Finance/Insurance | Operations Research/Decision Theory | Law of large numbers | Mathematical Biology in General | Secondary 60E07 | Primary 60F10 | STATISTICS & PROBABILITY | central limit theorem | law of large numbers | annealed asymptotics | parabolic Anderson model | quenched asymptotics | Submarine boats

Journal Article

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