On the mode-change problem for random measures.
On the moments of hitting times for random walks on trees.
On the moments of sums of independent identically distributed random variables.
On the multiple overlap function of the SK model.
In this note, we prove an asymptotic expansion and a central limit theorem for the multiple overlap R1, ..., s of the SK model, defined for given N, s ≥ 1 by R1, ..., s = N-1Σi≤N σ1i ... σsi. These results are obtained by a careful analysis of the terms appearing in the cavity derivation formula, as well as some graph induction procedures. Our method could hopefully be applied to other spin glasses models.
On the multiplicative ergodic theorem for uniquely ergodic systems
On the multivariate skew-normal distribution and its scale mixtures.
On the need to adapt de Finetti's probability interpretation to QM
von Neumann's reliance on the von Mises frequentist interpretation is discussed and compared with the Dutchbook approach proposed by de Finetti.
On the negative dependence in Hilbert spaces with applications
This paper introduces the notion of pairwise and coordinatewise negative dependence for random vectors in Hilbert spaces. Besides giving some classical inequalities, almost sure convergence and complete convergence theorems are established. Some limit theorems are extended to pairwise and coordinatewise negatively dependent random vectors taking values in Hilbert spaces. An illustrative example is also provided.
On the Newcomb-Benford law in models of statistical data.
We consider positive real valued random data X with the decadic representation X = Σi=∞∞Di 10i and the first significant digit D = D(X) in {1,2,...,9} of X defined by the condition D = Di ≥ 1, Di+1 = Di+2 = ... = 0. The data X are said to satisfy the Newcomb-Benford law if P{D=d} = log10(d+1 / d) for all d in {1,2,...,9}. This law holds for example for the data with log10X uniformly distributed on an interval (m,n) where m and n are integers. We show that if log10X has a distribution function...
On the noncoalescence of a two point brownian motion reflecting on a circle
On the non-convexity of the time constant in first-passage percolation.
On the non-equivalence of two criteria of comparability of stationary point processes
On the nonexistence of a law of the iterated logarithm for weighted sums of identically distributed random variables.
On the norms of the random walks on planar graphs
We consider the nearest neighbor random walk on planar graphs. For certain families of these graphs, we give explicit upper bounds on the norm of the random walk operator in terms of the minimal number of edges at each vertex. We show that for a wide range of planar graphs the spectral radius of the random walk is less than one.
On the notion of -completeness of a stochastic flow on a manifold.
On the Novikov-Shiryaev optimal stopping problems in continuous time.
On the number of collisions in lambda-coalescents.
On the number of ground states of the Edwards–Anderson spin glass model
Ground states of the Edwards–Anderson (EA) spin glass model are studied on infinite graphs with finite degree. Ground states are spin configurations that locally minimize the EA Hamiltonian on each finite set of vertices. A problem with far-reaching consequences in mathematics and physics is to determine the number of ground states for the model on for any . This problem can be seen as the spin glass version of determining the number of infinite geodesics in first-passage percolation or the number...
On the number of local extrema in a sequence of independent random variables
On the number of representations of an element in a polygonal Cayley graph
We compute explicitly the number of paths of given length joining two vertices of the Cayley graph of the free product of cyclic groups of order k.