According to the Nielsen-Ninomiya No-Go theorem, the doubling of fermions on the lattice cannot be suppressed in a chiral theory. Whereas Wilson and staggered fermions suppress doublers with explicit breaking of chiral symmetry, the random lattice does so by spontaneous chiral symmetry breaking even in the free theory. I present results for meson masses, the chiral condensate and fermionic eige...

We compute the exact rates of convergence in total variation associated with the ‘fourth moment theorem’ by Nualart and Peccati (2005), stating that a sequence of random variables living in a fixed Wiener chaos verifies a central limit theorem (CLT) if and only if the sequence of the corresponding fourth cumulants converges to zero. We also provide an explicit illustration based on the Breuer-M...

We use Poisson approximation techniques for sums of indicator random variables to derive explicit error bounds and central limit theorems for several functionals of random trees. In particular, we consider (i) the number of comparisons for successful and unsuccessful search in a binary search tree and (ii) internode distances in increasing trees. The Poisson approximation setting is shown to be...

According to the Nielsen-Ninomiya No-Go theorem, the doubling of fermions on the lattice cannot be suppressed in a chiral theory. Whereas Wilson and staggered fermions suppress doublers with explicit breaking of chiral symmetry, the random lattice does so by spontaneous chiral symmetry breaking even in the free theory. I present results for meson masses, the chiral condensate and fermionic eige...

We consider transient random walks in random environment on Z with zero asymptotic speed. A classical result of Kesten, Kozlov and Spitzer says that the hitting time of the level n converges in law, after a proper normalization, towards a positive stable law, but they do not obtain a description of its parameter. A different proof of this result is presented, that leads to a complete characteri...

We give an explicit extension of Spencer’s result on the biplanar crossing number of the ErdősRényi random graph G(n, p). In particular, we show that the k-planar crossing number of G(n, p) is almost surely Ω((np)). Along the same lines, we prove that for any fixed k, the k-planar crossing number of various models of random d-regular graphs is Ω((dn)) for d > c0 for some constant c0 = c0(k).

We consider the moment space Mn corresponding to p × p complex matrix measures defined on K (K = [0, 1] or K = T). We endow this set with the uniform law. We are mainly interested in large deviations principles (LDP) when n→∞. First we fix an integer k and study the vector of the first k components of a random element ofMn . We obtain a LDP in the set of k-arrays of p× p matrices. Then we lift ...

In a recent paper, Shah and Zaman proposed the rumor center as an effective rumor source estimator for rumor spreading on random graphs. They proved for a very general random tree model that the detection probability remains positive as the number of nodes to which the rumor has spread tends to infinity. Moreover, they derived explicit asymptotic formulas for the detection probability of random...

We obtain an explicit formula for the variance of number $k$-peaks in a uniformly random permutation. This is then used to asymptotic length longest $k$-alternating subsequence permutations. Also central limit proved latter statistic.