Randomness in Space and Time  Page description

Help  Print 
Back »
 

Details of project

  
Identifier
49835
Type NI
Principal investigator Fritz, József
Title in Hungarian Véletlen jelenségek térben és időben
Title in English Randomness in Space and Time
Panel Natural Sciences large proposals
Department or equivalent Department of Differential Equations (Budapest University of Technology and Economics)
Participants Andai, Attila
Balázs, Márton
Bálint, Péter
Farkas, Lóránt
Mosonyi, Milán
Nagy, Katalin
Petz, Dénes
Réffy, Júlia
Rudas, Anna
Simon, Károly
Szász, Domokos
Tóth, Bálint
Tóth, Imre Péter
Valkó, Benedek
Varjú, Tamás
Starting date 2005-01-01
Closing date 2008-12-31
Funding (in million HUF) 30.160
FTE (full time equivalent) 15.33
state closed project





 

Final report

  
Results in Hungarian
A statissztikus fizika és kvantummechanika matematikai problémáival foglalkozunk. A hidrodinamika mikroszkopikus modelljeinek tág osztályait vizsgáltuk, különös tekintettel hiperbolikus skálázású rendszerek makroszkopikus viselkedésére a lökéshulllámok tartományában. Levezettük a rugalmasságtan nemlineáris egyenleteit. Áttörést jelentő eredmények születtek aszimmetrikus modellek 1/3 kitevős skálázásával kapcsolatban (szubdiffúzív viselkedés). Erdős-Rényi-Barabási tipusú ömszervező strukturák kritikus viselkedését, a gráf komponenseinek aszimptokus méretét tisztáztuk. Nem-Markov bolyongások határeloszlását meghatározva meglepő különbséget tapasztaltunk az irányított és nem irányított élek eseteinél. Leírtuk véletlen mátrixok sajátértékeinek pomtfolyamatát. Sinai biliárdok és általánosabb kaotikus dinamikai rendszerek ergodikus viselkedését tisztáztuk, eredményesen tárgyaltuk a sikbeli Lorentz folyamat rekurrenciájának és Brown-közelítésének problémáját. Meghatároztuk iterált függvényrendszerek attraktorainak Hausdorff dimnenzióját, véletlen Cantor halmazok különbségét. Tisztáztuk a kvantummechanikai állapottér geometriájának kérdéseit. A kvantumrendszerek állapotbecsléseit vizsgálva azok megbízhatóságát jellemeztük. Algoritmust adtunk n-szintű rendszer "constrained" becsléseire, a becslési stratégia számítógépes vizsgálatára is sor került. A folytonos optimalizáció különféle algoritmusit konstruáltuk meg, tisztáztuk azok hatékonyságát.
Results in English
Mathematical problems of statistical physics and quantum mechanics are investigated. Various microscopic models of hydrodynamics are introduced, existence of hyperbolic scaling limits is prroven including the derivation of the equations of nonlinear elastodynamics. Fairly deep results have been obtained on the 1/3 exponent scaling of asymmetric systems (subdiffusive behaviour of the tagged particle). In case of Erdős-Rényi-Barabási type self-organized systems the size of the graph components has been determined. Investigating the limit distribution of non-Markovian random walks, a considerable difference in the behavior of models with directed and non-directed bonds has been observed. Characterization of the point process of eigenvalues of random matrices was presented. Ergodic behavior of Sinai billiards and of more general dynamical systems has been described, discussion of recurrence and Brownian approximation of the planar Lorentz gas has been completed. Hausdorff dimension of attractors of iterated maps has been calculated, difference of random Cantor sets was also studied. Geometry of quantum mechanical and reliability of estimators for the state of quantum mechanical systems has been investigated. Algorithms for constrained estimation for n-level quantum systems have been introduced and investigated by computer simulations. Various methods of continuous optimalization and their effectiveness was also studied.
Full text http://real.mtak.hu/2032/
Decision
Yes





 

List of publications

  
J. Fritz, K. Nagy and S. Olla: Equilibrium fluctuations for a system of harmonic oscillators with conservative noise, J. Statist. Phys. Vol. 122 (2006) 367--392, 2006
J. Fritz and B. Tóth: Hyperbolic systems: Hydrodynamic limits via PDE methods, Oberwolfach Reports Vol 2. 1199-1230, 2005
B. Valkó: Hydrodynamic limit of perturbation of a hyperbolic equilibrium point in two-component systems, Annales de l'Institut Henri Poincare--Probabilities et Statistiques 42:61--80, 2006
M. Balázs and F. Rassoul-Agha and T. Seppalainen: The random average process and random walk in a space-time random environment in one dimension, Communications in Mathematical Physics Vol. 266 (2006), 2006
P. Bálint and I.P. Tóth: Hyperbolicity in multy-dimensional Hamiltonian systems with applications to soft billiards, Discrete and Continuous Dynamical Systems, Series A, Vol. 15 (2006):37--59, 2006
P. Bálint and S. Gouezel: Limit theorems in the stadium billiard, Commun. Math.l Phys. Vol. 263 (2006):461--512, 2006
B. Solomyak and K. Simon: Visibility for self-similar sets of dimension one in the plane, Real Analysis Exchange 32:169--193, 2006
Y. Peres and K. Simon and B. Solomyak: Absolute continuity for random iterated function systems with overlaps, London Mathematical Society, submitted, 2006
M. Dekking and K. Simon: On the size of the algebraic difference of two random Cantor sets, Random Structures and Algorithms 32:205--222, 2008
Réffy Júlia: Asymptotics of Random Unitaries, Doktori Értekezés, BME, 2005
M. Balázs and F. Rassoul-Agha and T. Seppalainen: Cube root asymptotics for the totally asymmetric simple exclusion process, Communications in Mathematical Physics, submitted in 2006, 2006
J. Fritz and K. Nagy: Uniqueness of the Euler limit of one-component lattice gas models, ALEA Latin American Journal of Probability Vol. 1 (2006) 367--397, 2006
K. Nagy: Hydrodynamic Limits and And Equilibrium Fluctuations of Interacting Particle Systems, Doktori Értekezés, Dauphine University (Paris), 2006 május 31, 2006
T. Varju: Local Limit Theorems and Recurrence for the Planar Lorentz Process, Doktori Értekezés, BME 2006 december 21, 2006
A.H. Fan and K. Simon and H.R. Tóth: Contracting on average random IFS with repelling fixpoint, J. Statist. Phys. Vol. 122 (2006):169--193, 2006
F. Hofbauer and P. Raith K. Simon: Hausdorff dimension for some hyperbolic attractors with overlaps and without finite Markov partition, Ergodic Theory Dynam. Systems 27 (4) (2007) 1143-1165., 2007
T. Jordan and M. Pollicott and K. Simon: Hausdorff dimension for randomly perturbed self-affine attractors, Commun. Math. Phys. 270 (2007) 519-544, 2007
A. Manning and K. Simon: Subadditive pressure for triangular maps, Nonlinearity Vol. 20 (2007):133--149, 2007
M. Balázs and T. Seppalainen: Exact connections between current fluctuations and the second class particle in a class of deposition models, Preprint, The University of Wisconsin 2006, 2006
M. Balázs and T. Seppalainen: Order of current variance and diffusivity in the asymmetric simple exclusion process, Preprint, The University of Wisconsin 2006, 2006
P. Bálint and B. Tóth and I.P. Tóth: On the zero mass limit of tagged particle diffusion in the 1-d Rayleigh gas, Journal of Statistical Physics 127 (2007) 657-675, 2007
A. Rudas and B. Tóth and B. Valkó: Random trees and general branching processes, Processes, Random Structures and Algorithms 31 (2007) 186-202, 2007
J. Quastel and B. Valkó: $t^{1/3}$ superdiffusivitz of finite range asymmetric exclusion processes on Z, Commun. Math. Phys. 273 (2007) 379-393, 2007
T. M. Liggett and J.E. Steiff and B. Tóth: Statistical mechanical systems on complete graphs, infinite exchangeability, finiteextensions and a discrete moment problem, The Annals of Probability 35 (2007) 867-914, 2007
P. Bálint and I.P. Tóth: Exponential decay of correlations in multi-dimensional dispersing billiards, Ann. Inst. H. Poincare 9:1309--1369, 2008
P. Bachurin and P. Bálint and I.P. Tóth: Local ergodicity for systems with growth properties including multi-dimensional dispersing billiards, Israel Journ. Math. 167:155--176, 2008
K.M. Hangos, D. Petz, A. Szántó and F. Szöllősi: State tomography for two qubits using reduced densities, J. Phys. A. Gen. Vol. 39 (2006):10901--10907, 2006
H. Ono and D. Petz and A. Szántó: Quasi-orthogonal subalgebras of 4x4 matrices, Preprint, BME 2006, 2006
M. Dekking, K. Simon and B. Székely: The algebraic difference of two random Cantor sets, preprint, 2007
A. Andai: Volume of the quantum mechanical state space, J. Phys. A: Math. Gen. 39 (2006) 13641-13657, 2006
A. Andai: On the curvature of the quantum state space with pull-back metrics, Linear Algebra and its Applications, 2007
A. Andai: On the geometry of generalized Gaussian distributions, J. Multivariate Analysis, submitted, 2008
P. Móra: Hausdorff measure for Sierpinski gasket, preprint, 2008
A. Andai: Uncertainty principle with quantum Fischer information, Journal of Mathemativcal Physics, submitted, 2008
C. Bahadoran, J. Fritz and Katalin Nagy: Relaxation scheme for a creation-annihilation model, Preprint, 2007
J. Quastel and B. Valkó: A note on the diffusivity of finite-range asymmetric exclusion processes on Z, Progress in Probability 60:543-550, 2008
Lukity Anikó: Végtelen differenciálegyenlet - rendszerek stabilitásáról, Preprint, Alkalmazott Matematikai Lapok, 2008
M. Balázs and F. Rassoul-Agha, T. Seppalainen and S. Sethuraman: Existence of the zero range process and a deposition model with superlinear growth rates, The Annals of Probability 35 (2007) 431-455, 2007
M. Balázs, E. Cator and T. Seppalainen: Cube root fluctuation for the corner growth model associated to the exclusion process, Electronic Journal of Probability 11 (2006) 1094-1132, 2006
B. Ráth and B. Tóth: Self-organized criticality in a mean field forest fire model, Preprint, 2007
B. Tóth and B. Vető: Skorohod reflection of Brownian paths and BES, Acta Sci. Math. 73:781-788, 2007
B. Tóth and B. Vető: Self-repelling random walk with directed edges on Z, Electronic Journ. Probability. 13:1909--1926, 2008
Bence Tóth, B. Tóth and J. Kertész: Modelling the Epps effect of cross correlations in asset prices, Proceedings of SPIE 6601 (Fluctuations and Noise 2007), 2007
M. Balázs and T. Seppalainen: Exact connections between current fluctuations and the second class particle in a class of deposition models, Jounal of Statistical Physics 127 (2007) 431-455, 2007
M. Balázs and T. Seppalainen: A convexity property of expectations under expopnential weigths, Preprint, 2007
D. Szász and T. Varju: Limit laws and recurrence for the planar Lorentz process with infinite horizon, Journal of statistical Physics 129 (2007) 59-80, 2007
D. Dolgopyat, D. Szász and T. Varju: Algebro-geometric methods for hard ball systems, Discrete and Continuous Dynamical Systems, to appear, 2008
D. Dolgopyat, D. Szász and T. Varju: Limit theorems for perturbed Lorentz processes, Preprint, 2008
P. Gibliscio, F. Hiai and D. Petz: Quantum covariance, quantum Fisher information and the uncertainty principle, Preprint, 2008
J. Fritz:: Microscopic theory of isothermal elastodynamics, Preprint, TU Budapest, 2008
B. Tóth and B. Valkó: Particle systems with several conservation laws, Oberwolfach Reports Vol 2. 1199-1230, 2005
M. Balázs and T. Seppalainen: Order of current variance and diffusivity in the asymmetric simple exclusion process, Annales of Mathematics, accepted, 2009
M. Balázs and T. Seppalainen: Fluctuation bounds for the asymmetric simple exclusion process, Alea Latin American Journal of Probability, 2009
M. Balázs, J. Komjáthy and T. Seppalainen: Microscopic concavity and and fluctuation bounds in a class of deposition models, Preprint 2008, 2009
M. Balázs and J. Komjáthy: Order of current variance and diffusivitz in the rate one totally asymmetric yero range process, Journ. Statist. Phys. 133:59-78, 2008
J. Quastel and B. Valkó: KdV preserves white noise, Commun. Math. Phys. 277:707-714, 2008
B. Tóth and B. Valkó: Particle systems with several conservation laws, Oberwolfach Reports Vol 2. 1199-1230, 2005
I. Horváth, B. Tóth and B. Vető: Diffusive bounds for the myopic self-avoiding walk in three and more dimensions, Preprint, TU Budapest 2008, 2009
G. Amir, G. Angel and B. Valkó:: The TASEP speed process., Preprint 2008, 2009
B. Valkó and B. Virág:: Large gaps between random eigenvalues, Preprint 2008, 2009
B. Valkó and B. Virág:: Continuum limits of random matrices and the Brownian caroussel, Preprint 2008, 2009
B. Tóth and B. Vető:: Continuous time "true self-avoiding" random walk on Z., Preprint 2008, 2009
B. Tóth and B. Vető:: Self repelling random walk with directed edges., Electronic Journal of Probability 13:1909-1926, 2008
B. Ráth and B. Tóth: Triangular percolation in mean field random graphs - with PDE, Journal Statist. Phys. 131:385-391, 2008
B. Ráth and B. Tóth: Erdős-Rényi random graphs + forest fires = self-organized criticality, Preprint, TU Budapest 2008, 2009
M. Balázs and T. Seppalainen: A convexity property of expectations under exponential weights., Preprint 2007, 2009
P. Bálint, B. Tóth and P. Tóth:: On the zero mass limit oftagged particle diffusion in the 1-d Rayleigh gas, Journ. Statist. Phys. 127:657-675, 2007
B. Farkas: Hechler's theorem for analztic P-ideals, Preprint, TU Budapest 2008, 2009
I. Nagy, B. Kovács and J. Tóth: Detailed balance in ion channels: Application of Feinberg's theorem, Reaction Kinetecs and Catalysis Letters, accepted, 2009
Z. Molnár, I. Nagy, and T. Szilágyi: A change of variables theorem for the multidimensional Riemann integral, Ann. Sci. Uni. Budapest, submitted, 2009
B. G.-Tóth, F. Plastria, J. Fernandez and B. Pelegrin: On the impact of spatial pattern, aggregation and model parameters in planar Huff-like competitive location and design problems, OR Spectrum, DOI: 10.1007/s00291.008-0163-2, 2008
B. G.-Tóth and V. Kreinovich: Validated methods for computing Pareto sets: general algorithmic analysis, Int. J. Appl. Math. Comp.Sci. accepted, 2009
L.G. Casado, I. Garcia, B. G.-Tóth and E.M.T. Hendrix: On determining the cover of a simplex by spheres centered at its vertices, Preprint, TU Budapest, 2009
B. Torma and B. G.-Tóth: An efficient descent direction method with cutting planes, Preprint, TU Budapest, 2009
P. Móra: Estimate of the Hausdorff measure of the Sierpinski triangle, Fractals, accepted, 2009
P. Móra, K. Simon and B. Solomyak: The Lebesgue measure of the algebraic difference of two random Cantor sets, Preprint, TU Budapest, 2009
B. Balázs: Subadditive pressure for non-conformal maps, Preprint, TU Budapest, 2009
D. Petz, A. Szántó and M. Weiner: Complementarity and the algebraic structure of 4-level quantum systems, J. Infinite dimensional Anal. and Quantum Probability, accepted, 2009
J. Pitrik: Markov Property in the Noncommutative Probability, PhD dissyertáció, 2009
A. Jencova, D. Petz and J. Pitrik: Markov triplets on CCR algebras, Acta Sci. Math. (Szeged), accepted, 2009
D. Petz and J. Pitrik: Gaussian Markov Chains on CCR algebras, Preprint, TU Budapest, 2009
D. Szász and T. Varjú: Limit laws and recurrence for the planar Lorentz process with infinite horizon, J. Statist. Phys. 129:59--80, 2007
D. Dolgopyat, D. Szász and T. Varjú: Recurrence properties of the planar Lorentz process, Duke Math. Journal 142:241--281, 2008
D. Dolgopyat, D. Szász and T. Varjú: Theorems for perturbed Lorentz processes, Preprint, TU Budapest, 2009
D. Szász: Algebro-geometric methods for hard ball systems, Discrete and Continuous Dynamical Sysytems A. 22:427--443, 2009
B. Kovács: Rate based call gapping with priorities and fairness between traffic classes, IEEE/ACM-Transactions on Networks, accepted, 2009
B. Kovács: Modelling, characterization and Analzsis of token bucket as a call gapping mechanism with parameter setting proposals, Preprint, TU Budapest 2008, 2009
M. Balázs and J. Komjáthy: Order of current variance and diffusivity in the rate one totallz assymmetric zero range process, Journ. Statist. Phys. 133:59--78, 2008
M. Balázs, J. Komjáthy and T. Seppalainen: Microscopic concavity and fluctuation bounds in a class of deposition processes, Preprint, TU Budapest 2008, 2009
M. Balázs, J. Komjáthy and T. Seppalainen: Superdiffusivity and fluctuation bounds for the exponential bricklayer process, Preprint, TU Budapest 2008, 2009
M. Balázs and T. Seppalainen: Order of current variance and diffusivity in the asymmetric simple exclusion process, Annals of Mathematics, 2009
D. Szász: Some challenges in the theory of (semi)-dispersing billiards, Invited paper, Nonlinearity 21:187-193, 2008



Back »