Mark Kac

Q: What Schools Are Affiliated With Mark Kac

Mark Kac is affiliated with the following schools: Krzemieniec Lyceum, University of Southern California, Utrecht University, Rockefeller University, University of Lviv, Cornell University, Johns Hopkins University, University of Warsaw, Leiden University

Mark Kac's AcademicInfluence.com Rankings

Mark Kac

Mathematics

#204

Historical Rank

Probability Theory

#17

Historical Rank

Measure Theory

#142

Historical Rank

mathematics Degrees

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Mathematics

Why Is Mark Kac Influential?

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According to Wikipedia, Mark Kac was a Polish American mathematician. His main interest was probability theory. His question, "Can one hear the shape of a drum?" set off research into spectral theory, the idea of understanding the extent to which the spectrum allows one to read back the geometry.

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Mark Kac's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Toeplitz Forms And Their Applications (1958) (2512)
Probability and Related Topics in Physical Sciences (1960) (1086)
Can One Hear the Shape of a Drum (1966) (692)
Foundations of Kinetic Theory (1956) (653)
Statistical Mechanics of Assemblies of Coupled Oscillators (1965) (600)
The Spherical Model of a Ferromagnet (1952) (600)
On the van der Waals Theory of the Vapor‐Liquid Equilibrium. I. Discussion of a One‐Dimensional Model (1963) (577)
A stochastic model related to the telegrapher's equation (1974) (568)
On distributions of certain Wiener functionals (1949) (556)
Random Walk and the Theory of Brownian Motion (1947) (481)
On Some Connections between Probability Theory and Differential and Integral Equations (1951) (452)
On the notion of recurrence in discrete stochastic processes (1947) (369)
On an Explicitly Soluble System of Nonlinear Differential Equations Related to Certain Toda Lattices (1975) (321)
The Gaussian Law of Errors in the Theory of Additive Number Theoretic Functions (1940) (298)
A combinatorial solution of the two-dimensional Ising model (1952) (267)
On the Theory of Noise in Radio Receivers with Square Law Detectors (1947) (258)
Statistical Independence in Probability Analysis and Number Theory (1959) (257)
ON OCCUPATION TIMES FOR MARKOFF PROCESSES (1957) (253)
On certain limit theorems of the theory of probability (1946) (236)
A correction to “On the average number of real roots of a random algebraic equation” (1943) (223)
A Trigonometrical Series (1934) (215)
The ideal Bose-Einstein gas, revisited (1977) (212)
On Tests of Normality and Other Tests of Goodness of Fit Based on Distance Methods (1955) (199)
Relativistic Extension of the Analogy between Quantum Mechanics and Brownian Motion (1984) (198)
On the Eigen-Values of Certain Hermitian Forms (1953) (188)
An Explicit Representation of a Stationary Gaussian Process (1947) (179)
Toeplitz matrices, translation kernels and a related problem in probability theory (1954) (177)
On the Partition Function of a One‐Dimensional Gas (1959) (165)
A discrete version of the inverse scattering problem (1973) (160)
Large Excursions of Gaussian Processes (1959) (147)
On the Distribution of Values of Sums of the Type Σf(2 k t) (1946) (129)
On the Average Number of Real Roots of a Random Algebraic Equation (II) (1948) (128)
On the van der Waals Theory of the Vapor‐Liquid Equilibrium. III. Discussion of the Critical Region (1964) (122)
A complete solution of the periodic Toda problem. (1975) (115)
Some mathematical models in science. (1969) (113)
On the van der Waals Theory of the Vapor‐Liquid Equilibrium. II. Discussion of the Distribution Functions (1963) (111)
Study of Several Lattice Systems with Long‐Range Forces (1963) (109)
Probability methods in some problems of analysis and number theory (1949) (107)
On some periodic toda lattices. (1975) (100)
MATHEMATICAL MECHANISMS OF PHASE TRANSITIONS. (1969) (88)
On the number of positive sums of independent random variables (1947) (80)
On the Distribution of Values of Trigonometric Sums with Linearly Independent Frequencies (1943) (80)
Inequalities for Fourier transforms of positive functions (1945) (75)
Integration in function spaces and some of its applications (1980) (74)
Statistical Independence in Probability, Analysis and Number Theory. (1960) (72)
On Deviations between Theoretical and Empirical Distributions. (1949) (68)
On the average of a certain Wiener functional and a related limit theorem in calculus of probability (1946) (64)
Mathematics and logic (1979) (62)
On the Gaussian Law of Errors in the Theory of Additive Functions. (1939) (57)
A note on learning signal detection (1962) (55)
A gap theorem (1948) (54)
Mathematical Statistics and Probability (1962) (54)
WHAT IS RANDOM (1983) (51)
Enigmas of Chance: An Autobiography (1986) (49)
The Distribution of the Maximum of Partial Sums of Independent Random Variables (1950) (49)
A Sampling Method for Determining the Lowest Eigenvalue and the Principal Eigenfunction of Schroedinger's Equation (1950) (48)
Bose‐Einstein condensation in the presence of impurities. II (1973) (46)
An Elementary Queueing Problem (1962) (46)
Fluctuations and the Boltzmann equation. I (1976) (41)
Enigmas of Chance (1985) (40)
Critical Behavior of Several Lattice Models with Long‐Range Interaction (1969) (39)
Wiener and integration in function spaces (1966) (39)
On a Characterization of the Normal Distribution (1939) (36)
Random Walk in the Presence of Absorbing Barriers (1945) (35)
Propagation of Chaos and the Burgers Equation (1983) (34)
Some Probabilistic Aspects of the Boltzmann-Equation (1973) (33)
Selected Papers of Richard von Mises (1966) (30)
On the mathematical mechanism of phase transition. (1966) (27)
Ramanujan sums and almost periodic functions (1940) (27)
Phase Transition and Eigenvalue Degeneracy of a One Dimensional Anharmonic Oscillator (1969) (25)
Convergence and divergence of non-harmonic gap series (1941) (25)
Discrete thoughts: Essays on mathematics, science, and philosophy (1986) (23)
Sur les fonctions indépendantes (IV) (Intervalle infini) (1938) (22)
Statistical Analysis of Certain Types of Random Functions (1944) (22)
Helsinki final act. (1980) (22)
Gabor Szegö: Collected Papers (1982) (22)
James Gregory Tercentenary Memorial Volume. (1940) (20)
SPHERICAL MODEL AND THE INFINITE SPIN DIMENSIONALITY LIMIT. (1971) (19)
Une remarque sur les polynomes de M. S. Bernstein (1938) (19)
Some remarks on the use of probability in classical statistical mechanics (1956) (18)
POSSIBLE ORIGIN OF THE QUANTIZED VORTICES IN He II. (1972) (18)
Scattering length and capacity (1975) (17)
Distribution of eigenvalues of certain integral operators. (1955) (17)
Convergence of Certain Gap Series (1943) (17)
Basic stochastic processes : the Mark Kac lectures (1988) (17)
Probability Theory: Its Role and Its Impact (1962) (16)
On a theorem of Zygmund (1951) (16)
Remark on Recurrence Times (1959) (16)
The work of T.H. Berlin in statistical mechanics …a personal reminiscence (1964) (15)
Mark Kac : probability, number theory, and statistical physics : selected papers (1980) (15)
On applying mathematics Reflections and examples (1972) (14)
Correlation functions in the spherical and mean spherical models (1977) (13)
Hugo Steinhaus — A Reminiscence and a Tribute (1974) (13)
Sur les fonctions indépendantes (I) (Propriétés générales) (1936) (13)
Marginalia What is random ? (12)
A history-dependent random sequence defined by Ulam (1989) (12)
Sur les fonctions indépendantes (V) (1938) (12)
A formula for the pressure in statistical mechanics (1973) (11)
A CLASS OF LIMIT THEOREMS (1957) (11)
On Some Probabilistic Aspects of Classical Analysis (1970) (10)
Aspects probabilistes de la théorie du potentiel (1970) (10)
Husserl and the Reform of Logic (1992) (10)
Note on the distribution of values of the arithmetic function $d\left( m \right)$ (1941) (10)
Note on Power Series with Big Gaps (1939) (10)
Four papers on probability (1951) (9)
A probabilistic formula for the quantum N-body problem and the non-linear Schrödinger equation in operator algebra (1986) (8)
On rapidly mixing transformations and an application to continued fractions (1958) (8)
Topics in functional analysis : essays dedicated to M. G. Krein on the occasion of his 70th birthday (1978) (8)
A remark on Wiener’s Tauberian theorem (1965) (8)
Almost Periodicity and the Representation of Integers as Sums of Squares (1940) (8)
The Search for the Meaning of Independence (1982) (8)
Sur les fonctions indépendantes (II) (La loi exponentielle; la divergence de séries) (1936) (7)
On some isospectral second order differential operators. (1974) (7)
On a Series of Cosecants (1957) (7)
Mathematics and Logic: Retrospect and Prospects (1971) (7)
Review: P. M. Morse and H. Feshbach, Methods of theoretical physics (1956) (7)
On the Distribution of the Values of Real Almost Periodic Functions (1939) (6)
A remark on the theory of fluctuations far from thermodynamic equilibrium. (1977) (6)
Sur les fonctions indépendantes (III) (Le mouvement brownien; la loi de Maxwell) (1936) (6)
A Remark on Independence of Linear and Quadratic Forms Involving Independent Gaussian Variables (1945) (6)
CHAPTER 1 – Fluctuations* (1979) (6)
Signal and Noise Problems (1954) (6)
Misreading the History of Mathematics (1992) (6)
Some Remarks on Oscillators Driven by a Random Force (1960) (5)
Fluctuations Near and Far from Equilibrium (1977) (5)
Some mathematical problems in statistical mechanics (1969) (4)
ASYMPTOTIC BEHAVIOUR OF A CLASS OF DETERMINANTS (1969) (4)
Stochastic Processes and Their Application to the Theory of Cosmic Radiation (1950) (4)
THEOREMS ON LIFTING VECTOR-VALUED FUNCTIONS (1975) (3)
More Discrete Thoughts (1992) (3)
Translated functions and statistical independence (1941) (3)
Three body resonances in a coupled channel ND approach (1973) (3)
A Discrete Queueing Problem with Variable Service Times (1962) (3)
An application of probability theory to the study of Laplace's equation (1952) (3)
On some modified spherical models. (1975) (3)
Analysis of a Basic Queuing Problem Arising in Computer Systems (1961) (3)
Correction to the note: On rapidly mixing Transformations and an application to continued fractions (1959) (2)
Sur les Functions 2nt−[2nt]−½ (1938) (2)
Cours D'Analyse de l'Ecole Polytechnique, Tome III, Theorie des Equations. (1965) (2)
Marginalia. Statistical odds and ends. (1983) (2)
Probability of the pittsburgh deaths. (1977) (2)
Economics, Mathematical and Empirical (1992) (2)
Memoir of a physicist. (1979) (2)
A mathematician looks at medicine. (1979) (2)
Non-markovian diffusion in idealized Lorentz gases (1973) (2)
How I Became a Mathematician (1984) (2)
A Remark On The Preceding Paper By A. Rényi (1955) (1)
Mathematics and Its History (1992) (1)
William Feller, in memoriam (1972) (1)
Circular Equidistributions and Statistical Independence (1939) (1)
Corrections to the paper “Remarks on fluctuations of sums of independent random variables” (1953) (1)
Lectures on Mathematical Aspects of Phase Transitions (1973) (1)
A statistical method for determining the lowest eigenvalue of Schrodinger's equation (1952) (1)
Marginalia: Dehydrated Elephants Revisited (1982) (1)
When is random random (1983) (1)
Corrections to the Paper of a. Kurato and M. P. Kac (1976) (1)
On Buffon's Problem and Its Generalizations (1939) (1)
SOME REFLECTIONS OF A MATHEMATICIAN ON THE NATURE AND THE ROLE OF STATISTICS (1975) (1)
Nonlinear dynamics and inverse problems (1978) (1)
On the van der Waals Theory of the Vapor–Liquid Equilibrium. III. Discussion of the Critical Region (1966) (1)
Review: J. Neyman, Proceedings of the Berkeley Symposium on Mathematical Statistics and Probability (1950) (1)
The Wonderful World of Uncle Stan (1992) (0)
Singular perturbation in some problems of Statistical Mechanics (1972) (0)
Degrees revoked in soviet union. (1982) (0)
Soviet Arrests Continue (1975) (0)
Gabor Szegö Collected Papers. Edited by Richard Askey (1984) (0)
Statistical Independence in Probability, Analysis and Number Theory: FROM VIETA TO THE NOTION OF STATISTICAL INDEPENDENCE (1959) (0)
Will Computers Replace Humans (1992) (0)
On the van der Waals Theory of the Vapor–Liquid Equilibrium. I. Discussion of a One-Dimensional Model (1966) (0)
Lecture Series on Differential Equations. Session 7. Stochastic Differential Equations. (1969) (0)
On the Characteristic Functions of the Distributions of Estimates of Various Deviations in Samples from a Normal Population (1948) (0)
Doing Away with Science (1992) (0)
Letter from Mark Kac to Joshua Lederberg (1980) (0)
Une remarque sur les séries trigonométriques (0)
Some analytic aspects of probabilistic potential theory (1969) (0)
Soviet arrests continue. (1975) (0)
Statistics and Its History (1992) (0)
Quelques Remarques sur les Zeros des Intégrales de Fourier (1938) (0)
Can You Hear the Shape of a Drum (1974) (0)
Toeplitz Forms and Their Applications . Ulf Grenander and Gabor Szego. University of California Press, Berkeley, 1958. vii + 245 pp. $6. (1958) (0)
A legacy and a hope (1980) (0)
The Social Responsibility of the Academic Community (1975) (0)
On a problem concerning probability and its connection with the theory of diffusion (1940) (0)
Mathématiques et logique : rétrospective et perspectives (1973) (0)
Letter from Mark Kac, Joel Lebowitz, and Paul Plotz to Marshall W. Nirenberg (1983) (0)
Quelques Problèmes Mathématiques en Physique Statistique (1975) (0)
Yosif begun. (1984) (0)
The Three Body Toda System and A Parametrization of Plane Cubic Curves (1986) (0)
Letter from Mark Kac and Max Gottesman, Committee of Concerned Scientists, Inc. to Joshua Lederberg (1979) (0)
Review: Paul R. Halmos, Finite dimensional vector spaces (1943) (0)
Computer-Aided Instruction (1992) (0)
Degrees Revoked in Soviet Union (1982) (0)
Mark Kac Interview February 1978 (1978) (0)
Analytic Geometry and Calculus. (1947) (0)
Computing and Its History (1992) (0)
Review: L. P. Gokieli, On the So-Called "Content-Having Axioms" of Mathematical Logic (1942) (0)
The Future of Computer Science (1992) (0)
Stochastic processes in fluctuation theory (1976) (0)

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