相关论文: New matrix model solutions to the Kac-Schwarz prob…

We study two closely related families of varieties arising from genus $0$ stable maps to the Lagrangian Grassmannian $\operatorname{LG}(n,2n)$. First, we construct the Kausz--type compactification $\mathcal {TL}_n$ of the space of symmetric…

We consider a Neumann problem for strictly convex variational functionals of linear growth. We establish the existence of minimisers among $\operatorname{W}^{1,1}$-functions provided that the domain under consideration is simply connected.…

We identify the Kontsevich-Penner matrix integral, for finite size $n$, with the isomonodromic tau function of a $3\times 3$ rational connection on the Riemann sphere with $n$ Fuchsian singularities placed in correspondence with the…

Let $W\subset GL(V)$ be a complex reflection group, and ${\mathscr A}(W)$ the set of the mirrors of the complex reflections in $W$. It is known that the complement $X({\mathscr A}(W))$ of the reflection arrangement ${\mathscr A}(W)$ is a…

We study perturbations around the generalized Kazakov multicritical one-matrix model. The multicritical matrix model has a potential where the coefficients of $z^n$ only fall off as a power $1/n^{s+1}$. This implies that the potential and…

We consider matrix-model representations of the meander problem which describes, in particular, combinatorics for foldings of closed polymer chains. We introduce a supersymmetric matrix model for describing the principal meander numbers.…

We continue the analysis in [3] of matrix convex functions of a fixed order defined in a real interval by differential methods as opposed to the characterization in terms of divided differences given by Kraus [5]. We amend and improve some…

Existence and uniqueness of advanced and retarded fundamental solutions (Green's functions) and of global solutions to the Cauchy problem is proved for a general class of first order linear differential operators on vector bundles over…

In this paper, we present a minimal formalism for Stein operators which leads to different probabilistic representations of solutions to Stein equations. These in turn provide a wide family of Stein-Covariance identities which we put to use…

Since the ($\beta$-deformed) hermitian one-matrix models can be represented as the integrated conformal field theory (CFT) expectation values, we construct the operators in terms of the generators of the Heisenberg algebra such that the…

The quantisation of the Wess-Zumino-Witten model on a circle is discussed in the case of $SU(N)$ at level $k$. The quantum commutation of the chiral vertex operators is described by an exchange relation with a braiding matrix, $Q$. Using…

This is a brief review of recent progress in constructing solutions to the matrix model Virasoro equations. These equations are parameterized by a degree n polynomial W_n(x), and the general solution is labeled by an arbitrary function of…

We consider the quartic analogue of the Kontsevich model, which is defined by a measure $\exp(-{N}\,\mathrm{Tr}(E\Phi^2+(\lambda/4)\Phi^4)) d\Phi$ on Hermitian ${N}\times{N}$-matrices, where $E$ is any positive matrix and $\lambda$ a…

We use the contracting mapping principle for proving that under some mild restrictions the Cauchy problem for quasilinear systems of functional differential equations with retarded arguments has the unique solution. As a consequence from…

Riemann surfaces with nodes can be described by introducing simple composite operators in matrix models. In the case of the Kontsevich model, it is sufficient to add the quadratic, but ``non-propagating'', term (tr[X])^2 to the Lagrangian.…

We present a method to obtain infinitely many examples of pairs $(W,D)$ consisting of a matrix weight $W$ in one variable and a symmetric second-order differential operator $D$. The method is based on a uniform construction of matrix valued…

The Kazakov-Migdal model, if considered as a functional of external fields, can be always represented as an expansion over characters of $GL$ group. The integration over "matter fields" can be interpreted as going over the {\it model} (the…

We give a conjectural formula for sheaves supported on (irreducible) conormal varieties inside the cotangent bundle of the Grassmannian, such that their equivariant $K$-class is given by the partition function of an integrable loop model,…

We develop the theory of integrable operators $\mathcal{K}$ acting on a domain of the complex plane with smooth boundary in analogy with the theory of integrable operators acting on contours of the complex plane. We show how the resolvent…

We propose modified action which is equivalent to N=1 Green-Schwarz superstring and which allows one to realize the supplementation trick [26]. Fermionic first and second class constraints are covariantly separated, the first class…