The probability of large deviations for the sum functions of spacings.
The quenched invariance principle for random walks in random environments admitting a bounded cycle representation
We derive a quenched invariance principle for random walks in random environments whose transition probabilities are defined in terms of weighted cycles of bounded length. To this end, we adapt the proof for random walks among random conductances by Sidoravicius and Sznitman (Probab. Theory Related Fields129 (2004) 219–244) to the non-reversible setting.
The rate of convergence for spectra of GUE and LUE matrix ensembles
We obtain optimal bounds of order O(n −1) for the rate of convergence to the semicircle law and to the Marchenko-Pastur law for the expected spectral distribution functions of random matrices from the GUE and LUE, respectively.
The Rate of Convergence in the Functional Central Limit Theorem for Random Quadratic Forms with Some Applications to the Law of Iterated Logarithm.
The rate of convergence of option prices when general martingale discrete-time scheme approximates the Black-Scholes model
We take the martingale central limit theorem that was established, together with the rate of convergence, by Liptser and Shiryaev, and adapt it to the multiplicative scheme of financial markets with discrete time that converge to the standard Black-Scholes model. The rate of convergence of put and call option prices is shown to be bounded by . To improve the rate of convergence, we suppose that the increments are independent and identically distributed (but without binomial or similar restrictions...
The right tail exponent of the Tracy–Widom distribution
The Tracy–Widom distribution is the large dimensional limit of the top eigenvalue of random matrix ensembles. We use the stochastic Airy operator representation to show that as the tail of the Tracy–Widom distribution satisfies
The single server queue and the storage model: large deviations and fixed points.
The spectral laws of Hermitian block-matrices with large random blocks.
The strong law of large numbers for dependent vector processes with decreasing correlation: “Double averaging concept”.
The strong law of large numbers for -statistics with dependent data.
The strong law of large numbers for o-convergent random variables
The sum of digits of
The unconditional pointwise convergence of orthogonal seriesin over a von Neumann algebra
The paper is devoted to some problems concerning a convergence of pointwise type in the -space over a von Neumann algebra M with a faithful normal state Φ [3]. Here is the completion of M under the norm .
The unscaled paths of branching brownian motion
For a set A ⊂ C[0, ∞), we give new results on the growth of the number of particles in a branching Brownian motion whose paths fall within A. We show that it is possible to work without rescaling the paths. We give large deviations probabilities as well as a more sophisticated proof of a result on growth in the number of particles along certain sets of paths. Our results reveal that the number of particles can oscillate dramatically. We also obtain new results on the number of particles near the...
The von Neumann algebra associated with an infinite number of t-free noncommutative gaussian random variables
We show that the von Neumann algebras generated by an infinite number of t-deformed free gaussian operators are factors of type .
The weak convergence of regenerative processes using some excursion path decompositions
We consider regenerative processes with values in some general Polish space. We define their -big excursions as excursions such that , where is some given functional on the space of excursions which can be thought of as, e.g., the length or the height of . We establish a general condition that guarantees the convergence of a sequence of regenerative processes involving the convergence of -big excursions and of their endpoints, for all in a set whose closure contains . Finally, we provide...
The Wiener process and the central limit theorem.
The zero-one law for planar random walks in i.i.d. random environments revisited.
The Zero-one law for Products of Internal *-finitely Additive Probabiltty Spaces
Théorème central limite local sur certains groupes de Lie