Subproduct systems of Hilbert spaces: dimension two (2009)
A subproduct system of two-dimensional Hilbert spaces can generate an Arveson system of type I1 only. All possible cases are classified up to isomorphism. This work is triggered by a question of...
Graded algebras and subproduct systems: dimension two (2009)
Objects dual to graded algebras are subproduct systems of linear spaces, a purely algebraic counterpart of a notion introduced recently in the context of noncommutative dynamics (Shalit and Solel,...
Uniformly spread measures and vector fields (2008)
Sodin, Mikhail, Tsirelson, Boris
We show that two different ideas of uniform spreading of locally finite measures in the d-dimensional Euclidean space are equivalent. The first idea is formulated in terms of finite distance...
Moderate deviations for random fields and random complex zeroes (2008)
Moderate deviations for random complex zeroes are deduced from a new theorem on moderate deviations for random fields.
Divergence of a stationary random vector field can be always positive (a Weiss' phenomenon) (2007)
The divergence of a stationary random vector field at a given point is usually a centered (that is, zero mean) random variable. Strangely enough, it can be equal to 1 almost surely. This fact is...
Some extremal problems related to Bell-type inequalities (2007)
The best approximation by bounded product functions is calculated for some very simple two-valued functions of two variables.
Moderate deviations for log-like functions of stationary Gaussian processes (2007)
A moderate deviation principle for nonlinear functions of Gaussian processes is established. The nonlinear functions need not be locally bounded. Especially, the logarithm is allowed. (Thus, small...
Automorphisms of the type II_1 Arveson system of Warren's noise (2006)
Motions of the plane (shifts and rotations) correspond to automorphisms of the type I Arveson system of white noise. I prove that automorphisms corresponding to rotations cannot be extended to the...
How often is the coordinate of a harmonic oscillator positive? (2006)
The coordinate of a harmonic oscillator is measured at a time chosen at random among three equiprobable instants: now, after one third of the period, or after two thirds. The (total) probability that...
Brownian local minima, random dense countable sets and random equivalence classes (2006)
Tsirelson, Boris; Tel Aviv University; Tsirel@post.tau.ac.il
A random dense countable set is characterized (in distribution) by independence and stationarity. Two examples are `Brownian local minima' and `unordered infinite sample'. They are identically...
Brownian local minima, random dense countable sets and random equivalence classes (2006)
A random dense countable set is characterized (in distribution) by independence and stationarity. Two examples are `Brownian local minima' and `unordered infinite sample'. They are identically...
Random dense countable sets: characterization by independence (2005)
A random dense countable set is characterized (in distribution) by independence and stationarity. Two examples are `Brownian local minima' and `unordered infinite sample'. They are identically...
Brownian local minima and other random dense countable sets (2005)
We compare two examples of random dense countable sets, `Brownian local minima' and `unordered uniform infinite sample'. They appear to be identically distributed. A framework for such notions is...
Percolation, boundary, noise: an experiment (2005)
The scaling limit of the critical percolation, is it a black noise? The answer depends on stability to perturbations concentrated along a line. This text, containing no proofs, reports experimental...
On automorphisms of type II Arveson systems (probabilistic approach) (2004)
A counterexample to the conjecture that the automorphisms of an arbitrary Arveson system act transitively on its normalized units.
Nonclassical stochastic flows and continuous products (2004)
Contrary to the classical wisdom, processes with independent values (defined properly) are much more diverse than white noise combined with Poisson point processes, and product systems are much more...
Nonclassical stochastic flows and continuous products (2004)
Contrary to the classical wisdom, processes with independent values (defined properly) are much more diverse than white noises combined with Poisson point processes, and product systems are much more...
Tsirelson, Boris, Werner, Wendelin
Incluye bibliografía e índice
Random complex zeroes, III. Decay of the hole probability (2003)
Sodin, Mikhail, Tsirelson, Boris
By a hole we mean a disc that contains no flat chaotic analytic zero points (i.e. zeroes of a random entire function whose Taylor coefficients are independent complex-valued Gaussian variables, and...
Random complex zeroes, II. Perturbed lattice (2003)
Sodin, Mikhail, Tsirelson, Boris
We show that the flat chaotic analytic zero points (i.e. zeroes of a random entire function whose Taylor coefficients are independent complex-valued Gaussian random variables, and the variance of the...
Scaling Limit, Noise, Stability (2003)
Linear functions of many independent random variables lead to classical noises (white, Poisson, and their combinations) in the scaling limit. Some singular stochastic flows and some models of...
Non-Isomorphic Product Systems (2002)
Uncountably many mutually non-isomorphic product systems (that is, continuous tensor products of Hilbert spaces) of types II-0 and III are constructed by probabilistic means (random sets and...
Random complex zeroes, I. Asymptotic normality (2002)
Sodin, Mikhail, Tsirelson, Boris
We consider three models (elliptic, flat and hyperbolic) of Gaussian random analytic functions distinguished by invariance of their zeroes distribution. Asymptotic normality is proven for smooth...
The quantum algorithm of Kieu does not solve the Hilbert's tenth problem (2001)
Recently T. Kieu (arXiv:quant-ph/0110136) claimed a quantum algorithm computing some functions beyond the Church-Turing class. He notes that "it is in fact widely believed that quantum computation...
Filtered probability spaces (called "filtrations" for short) are shown to satisfy such a topological zero-one law: for every property of filtrations, either the property holds for almost all...
Spectral densities describing off-white noises (2001)
For the white noise, the spectral density is constant, and the past (restriction to (-\infty,0)) is independent from the future (restriction to (0,+\infty)). If the spectral density is not too far...
From slightly coloured noises to unitless product systems (2000)
Stationary Gaussian generalized random processes having slowly decreasing spectral densities give rise to product systems in the sense of William Arveson (basically, continuous tensor product systems...
From random sets to continuous tensor products: answers to three questions of W. Arveson (2000)
The set of zeros of a Brownian motion gives rise to a product system in the sense of William Arveson (that is, a continuous tensor product system of Hilbert spaces). Replacing the Brownian motion...
A non-Fock fermion toy model (1999)
Recent progress in mathematical theory of random processes provides us with non-Fock product systems (continuous tensor products of Hilbert spaces) used here for constructing a toy model for...
Trees, Not Cubes: Hypercontractivity, Cosiness, and Noise Stability (1999)
Schramm, Oded; Microsoft Research; Schramm@microsoft.com, Tsirelson, Boris; Tel Aviv University; Tsirel@math.tau.ac.il
Noise sensitivity of functions on the leaves of a binary tree is studied, and a hypercontractive inequality is obtained. We deduce that the spider walk is not noise stable.
Noise sensitivity on continuous products: an answer to an old question of J. Feldman (1999)
A relation between sigma-additivity and linearizability, conjectured by Jacob Feldman in 1971 for continuous products of probability spaces, is established by relating both notions to a recent idea...
Scaling limit of Fourier-Walsh coefficients (a framework) (1999)
Independent random signs can govern various discrete models that converge to non-isomorphic continuous limits. Convergence of Fourier-Walsh spectra is established under appropriate conditions.
Fourier-Walsh coefficients for a coalescing flow (discrete time) (1999)
A two-dimensional array of independent random signs produces coalescing random walks. The position of the walk, starting at the origin, after N steps is a highly nonlinear, noise sensitive function...
Trees, not cubes: hypercontractivity, cosiness, and noise stability (1999)
Schramm, Oded, Tsirelson, Boris
Noise sensitivity of functions on the leaves of a binary tree is studied, and a hypercontractive inequality is obtained. We deduce that the spider walk is not noise stable.
Trees, Not Cubes: Hypercontractivity, Cosiness, and Noise Stability (1999)
Noise sensitivity of functions on the leaves of a binary tree is studied, and a hypercontractive inequality is obtained. We deduce that the spider walk is not noise stable. Introduction For the...
Unitary Brownian motions are linearizable (1998)
Brownian motions in the infinite-dimensional group of all unitary operators are studied under strong continuity assumption rather than norm continuity. Every such motion can be described in terms of...
Decreasing sequences of $\sigma$-fields and a measure change for Brownian motion (1996)
Dubins, Lester, Feldman, Jacob, Smorodinsky, Meir, Tsirelson, Boris
Let $(F_t)_{t \geq 0}$ be the filtration of a Brownian motion $(B(t))_{t \geq 0}on $(\Omega,F,P)$. An example is given of a measure $Q \sim P$ (in the sense of absolute continuity) for which...
Decreasing sequences of $\sigma$-fields and a measure change for Brownian motion. II (1996)
Feldman, Jacob, Tsirelson, Boris
Sharpening the main result of the preceding paper, it is shown that if, $B_t,0 \leq t < \infty$ is a standard Brownian motion on $(\Omega,F,P)$, then for any $\varepsilon > 0$ there is a probability...