A5068725978- Stochastic processes and statistical mechanics
- Quantum chaos and dynamical systems
- Theoretical and Computational Physics
- Black Holes and Theoretical Physics
- Random Matrices and Applications
- Diffusion and Search Dynamics
- Mathematical Dynamics and Fractals
- Cosmology and Gravitation Theories
- Quantum Mechanics and Non-Hermitian Physics
- Quantum Chromodynamics and Particle Interactions
- Quantum and electron transport phenomena
- Stochastic processes and financial applications
- Statistical Mechanics and Entropy
- advanced mathematical theories
- Quantum many-body systems
- Cold Atom Physics and Bose-Einstein Condensates
- Spectral Theory in Mathematical Physics
- Advanced Combinatorial Mathematics
- Particle physics theoretical and experimental studies
- Physics of Superconductivity and Magnetism
- Advanced Mathematical Physics Problems
- Bayesian Methods and Mixture Models
- Advanced Thermodynamics and Statistical Mechanics
- Complex Systems and Time Series Analysis
- Financial Risk and Volatility Modeling
Université Paris-Saclay
1979-2022
Centre National de la Recherche Scientifique
1989-2022
Laboratoire de Physique Théorique et Modèles Statistiques
2009-2022
Sorbonne Université
2003-2017
Université Paris Cité
1980-2017
Université Paris-Sud
2004-2015
Institut Henri Poincaré
2004-2014
Laboratoire de Physique Théorique
1985-2008
Institut de Physique
1979-1998
Laboratoire de Probabilités et Modèles Aléatoires
1998
We present an exact solution for the distribution $P({h}_{m},L)$ of maximal height ${h}_{m}$ (measured with respect to average spatial height) in steady state a fluctuating Edwards-Wilkinson interface one dimensional system size $L$ both periodic and free boundary conditions. For case, we show that $P({h}_{m},L)={L}^{\ensuremath{-}1/2}f({h}_{m}{L}^{\ensuremath{-}1/2})$ all $L>0$, where function $f(x)$ is Airy describes probability density area under Brownian excursion over unit interval....
Using path-integral techniques, we compute exactly the distribution of maximal height ${H}_{p}$ $p$ nonintersecting Brownian walkers over a unit time interval in one dimension, both for excursions watermelons with wall, and bridges without all integer $p\ensuremath{\ge}1$. For large $p$, show that $⟨{H}_{p}⟩\ensuremath{\sim}\sqrt{2p}$ (excursions) whereas $⟨{H}_{p}⟩\ensuremath{\sim}\sqrt{p}$ (bridges). Our exact results prove previous numerical experiments only measured preasymptotic...
The paper deals with exponential functionals of the linear Brownian motion which arise in different contexts, such as continuous time finance models and one-dimensional disordered models. We study some properties these relation problem a particle coupled to heat bath Wiener potential. Explicit expressions for distribution free energy are presented.
We consider a particle moving in one-dimensional potential which has symmetric deterministic part and quenched random part. study analytically the probability distributions of local time (spent by around its mean value) occupation above within an observation window size t. In absence randomness, these have three typical asymptotic behaviors depending on whether is unstable, stable, or flat. These are shown to get drastically modified when switched on, leading loss self-averaging wide sample...
We compute exactly the mean perimeter and area of convex hull N independent planar Brownian paths each duration T, both for open closed paths. show that < L_N > = \alpha_N, \sqrt{T} <A_N> \beta_N T all T. The prefactors \alpha_N \beta_N, computed N, increase very slowly (logarithmically) with increasing N. This slow growth is a consequence extreme value statistics has interesting implication in ecological context estimating home range herd animals population size
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The second virial coefficient for a gas of anyons is computed (i) by discretising the two-particle spectrum through introduction harmonic potential regulator and (ii) considering problem in continuum directly heat kernel methods. In both cases result Arovas et al. (1985) recovered.
Massive scalar and spin 1/2 fields are considered on a two-dimensional space-time with constant background curvature in the presence of an external field. For each case, Euler–Heisenberg effective action pair creation rate their dependence both field is determined exactly.
The concept of Lyapunov exponent has long occupied a central place in the theory Anderson localisation; its interest this particular context is that it provides reasonable measure localisation length. also features prominently products random matrices pioneered by Furstenberg. After brief historical survey, we describe some recent work exploits close connections between these topics. We review known solvable cases disordered quantum mechanics involving point scatterers and discuss new case....
We show that the distribution of time delay for one-dimensional random potentials is universal in high energy or weak disorder limit. Our analytical results are excellent agreement with extensive numerical simulations carried out on samples whose sizes large compared to localization length (localized regime). The case small also discussed (ballistic provide a physical argument which explains quantitative way origin exponential divergence moments. occurrence log-normal tail finite size...
We study some transport properties of a one dimensional disordered system finite length N. In this particles are subject to random forces resulting both from thermal noise and fom quenched force F(x) which models the inhomogeneous medium. The latter is distributed as white with non-zero average bias. Imposing fixed concentration at end points chain yields steady current J(N) depends on environments {F(x)}. problem computing probability distribution P(J) over addressed. Our approach based...
The asymmetric diffusion of a particle in random one-dimensional medium can be described by model potential with positive spectrum closely linked to supersymmetric quantum mechanics. We obtain analytical expressions for the density states ρ(ε) (inverse relaxation time spectrum). This allows us compute averaged probability return at any time. At zero energy exhibits variety singular behaviours continuously varying exponent. corresponds different phases problem large time, including Sinaï's...
We study the statistics of near-extreme events Brownian motion (BM) on time interval [0,t]. focus density states (DOS) near maximum \rho(r,t) which is amount spent by process at a distance r from maximum. develop path integral approach to functionals BM, allows us full probability function (PDF) and obtain an explicit expression for moments, \langle [\rho(r,t)]^k \rangle, arbitrary integer k. also near-extremes constrained like bridge. Finally we present numerical simulations check our...