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A fundamental problem from computational learning theory is to well-reconstruct an unknown function on the discrete hypercubes. One classical result of this problem for the random query model is the l...
In this lecture, I will discuss how ``tilted interlacements’’ and ``solidification of porous surfaces’’, two specific realizations of the change-of-measure and coarse graining ideas respectively, prod...
We consider random walks (RW) in a one-dimensional i.i.d. random environment with jumps to the nearest neighbours. For almost all environments, we prove a quenched Local Limit Theorem (LLT) for the...
The XOR-satisfiability (XORSAT) problem requires finding an assignment of n Boolean variables that satisfy m exclusive OR (XOR) clauses, whereby each clause constrains a subset of the variables. We co...
We present a deterministic approximation algorithm to compute logarithm of the number of ‘good’ truth assignments for a random k-satisfiability (k-SAT) formula in polynomial time (by ‘good’ we m...
Consider a collection of random variables attached to the vertices of a graph. The reconstruction problem requires to estimate one of them given ‘far away’ observations. Several theoretical results (a...
We present a simple and efficient algorithm for randomly generating simple graphs without small cycles. These graphs can be used to design high performance Low-Density Parity-Check (LDPC) codes. ...
Gibbs states and the set of solutions of random constraint satisfaction problems.
Let X1, . . . ,Xn be a collection of iid discrete random variables, and Y1, . . . , Ym a set of noisy observations of such variables. Assume each observation Ya to be a random function of some a rando...
ESTIMATING AND UNDERSTANDING EXPONENTIAL RANDOM GRAPH MODELS。
UNSEPARATED PAIRS AND FIXED POINTS IN RANDOM PERMUTATIONS。
Abstract: In this paper we develop and apply methods for the spectral analysis of non-self-adjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous determini...
We consider a random walk in a random potential, which models a situ-ation of a random polymer and we study the annealed and quenched costs to perform long crossings from a point to a hyperplane. Thes...
We construct a time-consistent sublinear expectation in the setting of volatility uncertainty. This mapping extends Peng’s G-expectation by allowing the range of the volatility uncertainty to be stoch...

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